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The following table shows the probability distribution for a discrete random variable. X 11 14 16 19 21 23 24 29 P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08 The mean of the discrete random variable X is 18.59. What is the variance of X? Round your answer to the nearest hundredth.

Respuesta :

Because the random variable X is discrete, the variance of X is defined as
var(X) = 
[tex]var(X)= \Sigma\limits^{n}_{i=1}\, { p_{i} ( x_{i}- \mu)^{2}} \, dx [/tex]
where
p =  values of probability as given in the table.
μ = 18.59

Calculate the array (x - μ).
x-μ = [-7.59 -4.59 -2.59 0.41 2.41 4.41 5.41 10.41]
Calculate the array (x-μ)².
(x- μ)² = [57.6081 21.0681 6.7081 0.1681 5.8081 19.4481 29.2681 108.3681]
Calculate the array p*(x-μ)².
p*(x- μ)² = [4.0326 4.4342 1.1404 0.042 0.2904 0.7779 3.8049 8.6694]
Calculate the variance of X.
var(X) = 23.182

Answer: 23.18 (nearest hundredth)

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