The mean is E(X) = 1. The variance of a discrete random variable is given by: σ 2 = Var ( X) = ∑ ( x i − μ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. Definition Let be a continuous random variable. Explanation. Covariance primarily indicates the direction of a relationship and can be calculated by finding the expected value of the product of each variable’s deviations from its mean. Modified 5 years, 8 months ago. variance Variances. As you can see, the expected variation in the random variable \(Y\), as quantified by its variance and standard deviation, is much larger than the expected variation in the random variable \(X\). . The uniform distribution is characterized as follows. Standard deviation is a measure of how spread out the data is from its 3. Dec 15, 2023 · Key Takeaways: Zoning variances allow property owners to use their land or construct buildings in a way that deviates from existing zoning regulations. 5 - The Mean and Variance; Lesson 11: Geometric and Negative Binomial Distributions. Var(X + Y) = Var(X) + Var(Y) + 2Cov(X, Y) In particular, Cov(X, X) = Var(X), so. The average of the squared difference from the mean is the variance. The unnecessary hardship must be peculiar to the property, not general to the neighborhood or community. Variance is one way to measure the amount a random variable \varies" from its mean over successive trials. 2. It is used in the derivation of properties related to the covariance and correlation of random variables. Therefore, variance depends on the standard deviation of the given data set. The importance of using a sample size minus one (n-1) for a more accurate estimate is highlighted. The spectrum is measured optically. Central dispersion tells us how the data that we are taking for observation are scattered and distributed. Aug 11, 2019 · A variance is an exception to a zoning restriction that allows the use of the land outside the requirements of the zoning for that area. A case for rezoning includes the benefits of the requested variance, and the hardship imposed on the homeowner by the current rules. In this chapter, we look at the same themes for expectation and variance. Let and be two independent Bernoulli random variables with parameter . 3: Variance. It is calculated as σ x2 = Var (X) = ∑ i (x i − μ) 2 p (x i) = E (X − μ) 2 or, Var (X) = E (X 2) − [E (X)] 2. First-step analysis for calculating eventual probabilities in a stochastic process. Suppose X has the following probability mass function: f(x) = P(X = x) = {0. . Some of these properties can be proved using the material presented in previous lectures. Depending upon the type of data available, the variance and covariance can be found for both sample data and population data. There are two main types of zoning variances: use variances and area variances. Var(X + X) = Var(X) + Var(X) + 2Var(X) = 4Var(X) which is the same as you would have deduced from applying the rule. 3 and 3. Using The random variable being the marks scored in the test. Commented Mar 26, 2013 at 22:28 Variance dispersion properties of second-order response surface designs. A vaiance is likely to be granted for unusual circumstances such as an especially narrow lot or a stream on the property making it especially difficult to comply with the local zoning ordinance. Area variances allow property owners to build or construct something typically prohibited by physical zoning requirements. In the case of private property, zoning laws generally have to balance the right of individual property owners with the rights of neighbors and the common good of the community at large. Calculating probabilities for continuous and discrete random variables. In addition, you are not likely to be approved for a variance if your plans A random variable is a process for choosing a random number. Variance cannot be negative because its squares are either positive or zero. The variance of a random variable Xis unchanged by an added constant: var(X+C) = var(X) for every constant C, because (X+C) E(X+C) = X EX, the C’s cancelling. Let X be the number on the first card. If the purposes of a zoning ordinance are held in a bucket, and variances (leaks) are granted that compromise ordinance purposes, then over time the purposes of the ordinance are lost. Measure the variability in the given sample data. 1. Sample data = 12, 15, 16, 20, 25, 24, 23, 30, 35, 36, 42. Stat. In this section we shall introduce a measure of this deviation, called the variance. Covariance Matrix Formula. Thus, we can summarize some properties of Theorem. Proof. Thus, Standard Deviation = $\sqrt {Var ( X )}$. P(X = 1) = 0:2; P(X = 2) = 0:3; May 27, 2014 · Under current statutes, that stringent standard is no longer allowed. Let the mean of random variables X and Y be μ X and μ Y, respectively. Previous example. Var (k) = 0. 5 - Key Properties of a Negative Binomial Random Variable; 11. Let X 1, X 2, …, X n be a random sample of Jun 20, 2024 · This property of equal mean and variance is a distinctive characteristic of the Poisson distribution and simplifies its statistical analysis. The expected value, E(X) E ( X), is defined for discrete and for continuous random variables X X as follows: E(X) = ∑all x xP(X = x) = ∑ xP(x) E ( X) = ∑ all x x P ( X = x) = ∑ x P ( x) E(X) = ∫ all x xf(x)dx E ( X) = ∫ all x x f ( x) d x. A property owner can prove unnecessary hardship, even if the owner has some reasonable use of the property without the variance. The above property says that the probability that the event happens during a time interval of length is independent of how much time has already May 23, 2024 · covariance, measure of the relationship between two random variables on the basis of their joint variability. Mar 30, 2021 · A use variance, on the other hand, involves a request by an owner to use the subject property in a way that is not permitted in the zoning district in which the property is situated. Let X2 = X1 X 2 = X 1. If is the covariance matrix of a random vector, then for any constant vector ~awe have ~aT ~a 0: That is, satis es the property of being a positive semi-de nite matrix. Two random variables x and y are independent if E (xy) = E (x)E (y). com Dec 21, 2023 · This work presents an original method based on the variance properties of the fluorescence spectrum emitted by an ensemble of nitrogen vacancy centers in diamond. A property owner can seek a variance for any number of reasons. See examples of coin flips, disk drive failures, and RAID systems. The covariance of two equal random The variance of a random variable tells us something about the spread of the possible values of the variable. The expected value of a discrete random variable is equivalent to a weighted mean, as can be Jan 20, 2024 · 1. 4. Theorem. Area and use variances are the most frequently requested variances. The mean, μ, of a discrete probability function is the expected value. If X(ω) is the observed value of X, its variation from the mean is X(ω) − μX. 05 ≈ 1. One useful result about variances which is relatively easy to show is that because the variance gives a measure or the square of the width of a distribution, the variance of a constant times a random variable is the square of the constant times the variance of the random variable . Let c 1 and c 2 be constants and u 1 and u 2 be functions. 1 The Autocorrelation and Autocovariance Functions. Solution –. = sample mean. In the Solved Problems section, we calculate the mean and variance for the gamma distribution. SD ( X) = σ X = Var ( X). Poisson Distribution Mean Mean of a Poisson distribution is also known as Poisson Distribution expected value or average of the distribution and is represented by “E[X]” or “λ” (lambda). Mean is the average of a given set of numbers. Thus the variance of \(X\) also fails to exist. +254 (0) 797 506 575 +254 (0) 738 350 493 Church Rd, Rongai Business Center, info@varianceproperties. In words, the variance is the expected squared difference between a random variable and its mean. For instance, you could obtain an area variance for the purpose of constructing a building that’s larger than the square-footage restrictions set by the zoning board. We delve into measuring variability in quantitative data, focusing on calculating sample variance and population variance. Var(X) = E (X E(X))2 The positive square root of the variance of a variate X is known as its standard deviation and is denoted by σ. It shows the distance of a random variable from its mean. The range is easy to calculate—it's the difference between the largest and smallest data points in a set. For example: Var (X) ≥ 0. Step 1: First of all, find the sample average value by taking the quotient of the sum of observations and the total number of data values. That the Variance does not authorize a use or activity which is not otherwise expressly authorized by the zoning regulations for the zoning district in which the subject property is located. Variance is a measure of how data points differ from the mean. Variances can be given by a locality for businesses who present valid reasons for the variance and who can show that the variance will not lessen property values or interfere with the use of the property by current residents. Then, when the mathematical expectation E exists, it satisfies the following property: E [ c 1 u 1 ( X) + c 2 u 2 ( X)] = c 1 E [ u 1 ( X)] + c 2 E [ u 2 ( X)] Before we look at the proof, it should be noted that the above property can be extended to more than two terms. deep) has low bias and high variance. Properties of Expected values and Variance Christopher Croke University of Pennsylvania Math 115 UPenn, Fall 2011 Christopher Croke Calculus 115. Let Y be the number on the last card. is the time we need to wait before a certain event occurs. μ = ∑(x ∙ P(x)) The standard deviation, Σ, of the PDF is the square root of the variance. For X X and Y Y defined in Equations 3. A variance allows a property to be used in a manner forbidden by the zoning ordinance. Exercise 1. Peculiar to the Property. SD(X) = σX = Var(X)− −−−−−√. We conduct a quantitative comparison of the ensemble's optical signal in both the visible and near infrared range. Modified 3 years, 9 months ago. A variance is different from a conditional use permit, because when a property owner is granted a variance he is allowed to use his property in a way that is otherwise forbidden by the ordinance. The variance of a random variable shows the variability or the scatterings of the random variables. variance of a random variable is called its standard deviation, sometimes denoted by sd(X). The difference between X and E(X) is either + 1 or − 1 , with. ∫∞ 0 λαxα−1e−λx Γ(α) dx = 1. Variance of sum of two random variables. As for a use variance, it allows To solve this issue, we define another measure, called the standard deviation , usually shown as σX σ X, which is simply the square root of variance. Χ = each value. ∫ 0 ∞ λ α x α − 1 e − λ x Γ ( α) d x = 1. The covariance inherits many of the same properties as the inner product from linear algebra. 1 - Geometric Distributions; 11. Mean and variance are measures of central dispersion. Property 9: V (a 1 X 1 + a 2 X 2 + … + a n X n) = a 1 2 V(X 1) + a 2 2 V(X 2) + … + a n 2 V(X n). The converse is NOT true. Jul 31, 2023 · 6. It provides property owners with the opportunity to seek relief when strict adherence to zoning ordinances would create an undue hardship or substantial practical difficulty. Can we derive a variance formula in terms of variance and expected value of X? $\endgroup$ – damla. Jan 7, 2022 · Rezoning. We will learn about different properties, but Covariance - Properties. The standard deviation of X is the square In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Find out the formulas, properties and examples of population and sample variance for grouped and ungrouped data. , show that for α, λ > 0 α, λ > 0, we have. Examine your construction plans, and determine if there is any way they can be revised so that a variance is not necessary. Intuitively, the covariance matrix generalizes the notion of variance to multiple The variance of a random variable X is the mean square of its variation about the mean value: Var [X] = σ2 X = E[(X − μX)2] where μX = E[X] The standard deviation for X is the positive square root σX of the variance. Example 1: For Sample Variance. Remarks. variance of any linear combination of X 1;:::;X p. Let be a normal random variable with mean and variance . The probability mass function of is The probability mass function of is The support of (the set of values can take) is The convolution formula for the probability mass function of a sum of two Sep 7, 2020 · Variability is also referred to as spread, scatter or dispersion. Jun 11, 2024 · Learn about variance, a statistical measure of how data is spread around the mean. Given a constant a a and random variables X X, Y Y, and Z Z, the following properties hold: \text {Cov} (X + Y, Z) = \text {Cov} (X, Z [The Variance is necessary to enjoy a basic property right available to other similarly-zoned properties in the vicinity. I want to know where the covariance goes in the other case. If all of the data points are the same, the variance is zero (Var(X) = 0). e. Recall also that by taking the expected value of various transformations of the variable, we can measure other interesting characteristics of the distribution. 4 - Negative Binomial Distributions; 11. It arises when a normal random variable is divided by a Chi-square or a Gamma random variable. One of the most important properties of the exponential distribution is the memoryless property : for any . Then sum all of those values. Variance attorneys work with property owners to assess the feasibility of their variance requests and develop and present compelling arguments supporting their requests to the local zoning board. Oct 16, 2020 · Properties of variance. Var (XY) plays a role in proving the Cauchy-Schwarz inequality, which has wide-ranging applications in various mathematical fields. We have done some of it below, and we expect that you can fill in the rest. For a random variable expected value is a useful property. n = number of values in the sample. g. Jul 15, 2023 · A variance is a form of equitable relief allowing the applicant to use his land in an efficient way by bypassing the local zoning laws. Cov(X,Y) =E[XY] −E[X]E[Y]. 6 - Negative Binomial Examples In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector . The variance Var (x) of a random variable is defined as Var (x) = E ( (x - E (x) 2 ). Obtaining a zoning variance involves submitting an application, paying a fee, and attending hearings and meetings Properties of Covariance# Let’s examine how covariance behaves. § 462. = sum of…. Apr 25, 2024 · A variance in real estate is an exception to a zoning law. The video, Role of the Zoning Board, can help you understand 2 days ago · Learn how to measure deviation in a probability distribution using variance, a statistic that is always non-negative. The probability mass function of X is. 11. Compute the variance of X, Y , Z. 2 . To determine the covariance matrix, the formulas for variance and covariance are required. The scale of the data influences variance. In general, it can be more difficult to obtain a use variance than a dimensional variance, as courts regard use variances as a complete deviation from the Variance of a sum: One of the applications of covariance is finding the variance of a sum of several random variables. A variance is a way for a city to allow an exception to part of a zoning ordinance. Establishing properties of covariance involves simple observations and routine algebra. Variance Another common property of random variables we are interested in is the Variance which measures the squared deviation from the mean. Conditional probability: P(A | B). Richmond, VA 23261, USA (Received September 1993; final version received March 1994) Abstract For the United States economy (1960-1989), the correlation Jan 3, 2024 · Variance: A variance is a legal mechanism that allows for a deviation from the strict application of zoning regulations. 0247. Although its properties make covariance useful in Variance of a random variable X Let E(X) = (The Greek letter \mu"). Area variance: An area variance allows you to make physical changes to your property that zoning requirements otherwise wouldn’t permit. Variance means to find the expected difference of deviation from actual value. Apr 23, 2022 · 4. An example where this is not true: Let Var(X1) = 1 Var ( X 1) = 1. Finn Research Department, Federal Reserve Bank a/Richmond. The variance of a constant value is equivalent to zero. Variance: average of squared distances from the mean. The square root of the variance of a random variable is called itsstandard deviation. ⁄ †standard deviation As with expectations, variances and covariances can also be calculated conditionally on various pieces of information. For ex- Jul 25, 2023 · Variance of XY (Var (XY)) is an essential measure in probability theory and statistics. Another measure of spread is the standard deviation, the square root of the variance. Population Variance: var (x) = ∑n 1 (x−μ)2 n ∑ 1 n ( x i − μ Memoryless property. 6(2). Dec 4, 2015 · The more general formula for the variance of a sum of two random variables is. Properties of a Variance. Jan 3, 2024 · A zoning variance is a legal exception granted to a property owner or developer, allowing them to deviate from certain zoning regulations that would otherwise apply to their property. , in hypothesis tests about the mean ). Variance remains invariant when a constant value is added to all the figures in the data set. A random variable having a uniform distribution is also called a uniform random Using the properties of the gamma function, show that the gamma PDF integrates to 1, i. ~aT ~ais the variance of a random variable. ∫-∞∞ p (x) dx = 1. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n 31. We answer this question using properties of covariance: Var[aX] = Cov[aX, aX] (Covariance-Variance Relationship) = a ⋅ a ⋅ Cov[X, X] (Pulling Out Constants) = a2Var[X] (Covariance-Variance Relationship) It makes sense that the variance should scale by a2a2, since the variance is in squared units. The board weighs all the pros and cons, and the homeowners’ stated Jun 23, 2023 · Definition: Standard Deviation. They have the burden of proof. 2: Variance of Discrete Random Variables. Our team of young professionals ensures that property owners optimizes function and returns from property assets. It is most commonly measured with the following: Range: the difference between the highest and lowest values. Oct 25, 2012 · Minn. Range, variance, and standard deviation all measure the spread or variability of a data set in different ways. This suggests the question: Given a symmetric, positive semi Properties of Variance. Let’s start with rezoning, but first, a quick caveat: although there are two types of rezoning actions, (1) an amendment to the zoning ordinance’s text that impacts all properties, or (2) an amendment to the ordinance’s map to change the use district of an individual parcel, because the first action is less common, this article will consider only the second. The mathematical expectation is denoted by the formula: E(X)= Σ (x 1 p 1, x 2 p 2, …, x n p n), where, x is a random variable with the probability function, f(x), 10. Tomas Alberto Arias Wed Sep 19, 2022 · The homeowners set forth the needs for rezoning. Densities whose variance is not defined, like the Cauchy density, behave quite differently in a number of important respects from those whose variance is finite. E(X) is the expected value and can be computed by the summation of the overall distinct values that is the random variable. Example on Variance of Random Variable 1] A fair six-sided die can be modeled as a discrete random variable, X, with outcomes 1 through 6, each with equal probability 1/6. 2. f. Definition: Given a random variable, X, the positive square root of the variance is called the standard deviation of X, denoted by SD[X] or σ. Standard deviation is the square root of the variance. Oct 31, 2018 · Properties of conditional variance. 4, we have. First of all, we need to express the above probability in terms of the distribution function of : Then, we need to express the distribution function of in terms of the distribution function of a standard normal random variable : Covariance has the following important properties: Covariance is equal to the expected value of the product minus the product of the expected values. The proof involves straightforward algebra and is left as an exercise for the reader. We also denote the mean of X + Y as μ X + Y. We shall see one instance of this difference in Section 8. Ask Question Asked 3 years, 9 months ago. Expected value The variance of X, denoted Var(X), is de ned by Var(X) = E[(X )2]. Compute the following probability: Solution. The Student's t distribution is a continuous probability distribution that is often encountered in statistics (e. 4 - Mean and Variance of Sample Mean. 1 The autocovariance function of a series (Xt) is defined as. A compact and simple device is designed to optimize the photon collection. For an example of a situation involving area variance, let’s say you’re buying a house and want to put up a fence. Then Var(X1 + X2) = Var(2X1) = 4 Var ( X 1 + X 2) = Var ( 2 Suggested Answer: In decision trees, the depth of the tree determines the variance. γx(t, t + h) ≡ cov(Xt, Xt + h), where the definition of covariance is given by: cov(Xt, Xt + h) ≡ E[XtXt + h] − E[Xt Dec 28, 2020 · When requesting a variance, property owners must take great care. Prof. The usefulness of the expected value as a prediction for the outcome of an experiment is increased when the outcome is not likely to deviate too much from the expected value. variance is always positive because it is the expected value of a squared number; the variance of a constant variable (i. We will introduce the autocorrelation function by first defining the autocovariance function. Var (X) = E [ (X – m) 2 ] where m is the expected value E (X) This can also be written as: Var (X) = E (X 2) – m 2. For example, suppose X is a fair coin flip: it takes values 0 and 1 with equal probability. So, in Kane County, property owners must show their request meets the above criteria by showing that the variance will not: Impair the access to light and air for the surrounding properties; Increase fire hazards or other hazards to surrounding 24. Interquartile range: the range of the middle half of a distribution. Find SD[X]. Viewed 178 times 0 $\begingroup$ I was doing the following question: Basic Properties of the Variance. We introduced above the formula Var(X) = E[(X )2]. A dimensional variance is for a use which is permitted in the zoning district, but which does not meet setback, area, height, location or similar requirements of the zoning ordinance. Solution. Put the cards in a random order. 22/31 by Marco Taboga, PhD. by Marco Taboga, PhD. Var(X) = E (X )2 The average (squared) di erence from the average. 3 - Geometric Examples; 11. We'll finally accomplish what we set out to do in this lesson, namely to determine the theoretical mean and variance of the continuous random variable X ¯. In doing so, we'll discover the major implications of the theorem that we learned on the previous page. In the formula, squaring the differences emphasises the deviations and makes the variance scale Jul 31, 2023 · diverges. According to Layman, a variance is a measure of how far a set of data (numbers) are spread out from their mean (average) value. Mar 22, 2023 · A variance attorney is a legal professional specializing in land use and zoning laws and helps clients navigate the process of obtaining a variance. Explore the properties of variance, such as linearity, additivity and scaling, with examples and worked problems. Ask Question Asked 5 years, 8 months ago. m. In other words, Standard deviation looks at how spread out a group of numbers is from the mean, by looking at the square root of the variance. This work presents an original method based on the variance properties of the microwave absorption spectrum of an ensemble of nitrogen vacancy centers in diamond. These formulas are given below. Often, second-order response surface designs are chosen on the basis of a single-valued criterion such as D- or G-optimality. The standard deviation of X X has the same unit as X X. 5, if x = − 1, 1 0, otherwise. There is an easier form of this formula we can use. A complicated decision tree (e. 3. Viewed 1k times 2 $\begingroup$ Full statement of So, if the covariances average to 0 0, which would be a consequence if the variables are pairwise uncorrelated or if they are independent, then the variance of the sum is the sum of the variances. 2 2. Derive the probability mass function of their sum. 357 subd. Typically requested by homeowners, an area variance is the most popular type of variance. For a discrete random variable X, the variance of X is written as Var (X). Contents. Sample variance. , a variable that always takes on the same value) is zero; in this case, we have that , and ; the larger the distance is on average, the higher the variance. While such criteria provide a useful basis for selecting designs, they often fail to convey the true nature of the design's sup. Var (X + k) = Var (X) If the values are multiplied Apr 9, 2018 · Know the difference between a dimensional variance and a use variance. We relieve you off the stress of legal Jan 18, 2023 · When you collect data from a sample, the sample variance is used to make estimates or inferences about the population variance. 2 - Key Properties of a Geometric Random Variable; 11. Try not to confuse properties of expected values with properties of variances. The standard deviation of a random variable is defined by σ x = √ Var (x) . Since a binomial variable X can be thought of as the sum of n independent Bernoulli trials (each with variance p (1 − p)), the variance of X is n times the variance of a single Bernoulli trial, thanks to the property that the variance of the sum of independent variables is the sum of their variances. The distinction between sample mean and population mean is also clarified. It is a desirable property that the spread should not be a ected by a change in location. Zoning regulations are put in place by local governments to control land use and ensure compatibility between different types of properties within a particular area. A use variance is a request to put the property to a use not permitted in the zoning district. Recall the expected value of a real-valued random variable is the mean of the variable, and is a measure of the center of the distribution. In the next two sections we will use our observations to calculate variances of sample sums. Let its support be a closed interval of real numbers: We say that has a uniform distribution on the interval if and only if its probability density function is. Given the p. Asymptotic theory (statistics) In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Definition 3. Let Z be the minimal number on the first 3 cards. And, yes, at. The sample variance formula looks like this: Formula. The expectation of a random variable is the long-term average of the The standard deviation of X is the square root of this sum: σ = √1. Variance Properties is a real estate company incorporated in Kenya, to undertake property management, property letting, property purchase, property sales and property consultancy services. Jul 1, 1995 · ELSEVIER 19 (1995)1249-1281 ___^__ Variance properties of Solow's productivity residual and their cyclical implications* Mary G. Informally, the expected value is the arithmetic mean of the possible values a random variable can take, weighted by the Mar 21, 2015 · I know that the variance of the difference of two independent variables is the sum of variances, and I can prove it. Aug 31, 2020 · An area variance allows the property owner to construct a building that goes against the physical requirements held within a zoning ordinance. ] No unauthorized use. s of the two random variables, this result should not be surprising. By combining the properties, we can derive 1. This lecture discusses some fundamental properties of the expected value operator. Standard deviation: average distance from the mean. If X X and Y Y are independent, then cov(X,Y) c o v ( X, Y) = 0. A compact and simple device is Learn how to calculate the variance of the sum or difference of independent random variables, and how to apply the binomial theorem to find the mean and variance of binomial distributions. Others are gathered here for convenience, but can be fully understood only after reading the material presented in subsequent lectures. Mean and Variance. Cov ( X, Y) = E [ X Y] − E [ X] E [ Y]. Note: In statistics and machine learning, the biasג€"variance tradeoff is the property of a set of predictive models whereby models with a lower bias in parameter estimation have a higher variance of the parameter estimates across Jul 12, 2022 · Think of a variance like an override or exception to a law. If you can modify your plans so that they conform to the local zoning ordinances, you will save yourself the hassle of applying for a variance. The variance of the sum of two random variables X and Y is: V ( X + Y) = V ( X) + V ( Y) + 2 ⋅ cov ( X, Y) Where cov ( X, Y) is the covariance of X and Y. Example 9. People with an interest in the outcome can raise objections against requested zoning variances. Variance has various essential characteristics, including: Variance is always a positive number (Var(X) 0). = sample variance. Var(aX) = a2Var(X) Var(2X) = 4Var(X) Below are a few examples of variance. As laws get passed for a reason, there also must be a good reason for an exception to a rule. Let X be a random variable with mean . It’s a measure of how spread out the distribution is. Corollary 6. au rg ri oi vj of zt fg cw qo