v x statistics formula V X 13 75 3 25 2 3 1875 It can be shown that if a and b are constants then V a bX b2V X In other words adding a constant a to a random variable does not change its variance and multiplying a random variable by a constant b causes the variance to be multiplied by b2
The variance of a random variable tells us something about the spread of the possible values of the variable For a discrete random variable X the variance of X is written as Var X 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 The standard deviation of X is the square Variance is a measure of dispersion meaning it is a measure of how far a set of numbers is spread out from their average value It is the second central moment of a distribution and the covariance of the random variable with itself and it is often represented by or 1
v x statistics formula
v x statistics formula
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Statistics Formula Sheet With Explanation Salonlassa
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Statistics Formula Sheet
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Revised on June 21 2023 The variance is a measure of variability It is calculated by taking the average of squared deviations from the mean Variance tells you the degree of spread in your data set The more spread the data the larger the variance is in relation to the mean Solution The variance of X is calculated as X 2 E X 2 3 4 2 0 3 4 4 2 0 4 5 4 2 0 3 0 6 And therefore the standard deviation of X is X 0 6 0 77 Now the variance of Y is calculated as
The formula to find the variance is given by Var X E X 2 Where Var X is the variance E denotes the expected value X is the random variable and is the mean Q4 How to find the variance easily De nition The variance of a random variable X with expected value EX is de ned as var X E X 2 The square root of the variance of a random variable is called its standard deviation sometimes denoted by sd X 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
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Now by replacing the sum by an integral and PMF by PDF we can write the definition of expected value of a continuous random variable as EX xfX x dx Let X Uniform a b Find EX Let X be a continuous random variable with PDF fX x 2x 0 x 1 0 otherwise Find the expected value of X Remember the law of the To find the expected value E X or mean of a discrete random variable X simply multiply each value of the random variable by its probability and add the products The formula is given as E X x P x E X x P x Here x represents values of the random variable X P x represents the corresponding probability and symbol
The standard deviation SD of X is The quantity h X X 2 is the squared deviation of X from its mean and 2 is the expected squared deviation i the weighted average of squared deviations where the weights are probabilities from the distribution If most of the probability distribution is close to then 2 will be The formula for the expected value of a continuous random variable is the continuous analog of the expected value of a discrete random variable where instead of summing over all possible values we integrate recall Sections 3 6 3 7 For the variance of a continuous random variable the definition is the same and we can still use the alternative formula
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v x statistics formula - The formula to find the variance is given by Var X E X 2 Where Var X is the variance E denotes the expected value X is the random variable and is the mean Q4 How to find the variance easily