I do not how to calculate the standard deviation Given the probability distribut

Question

I do not how to calculate the standard deviation

Given the probability distributions shown to the right, complete the following parts. Compute the expected value for each distribution. Compute the standard deviation for each distribution. Compare the results of distributions A and B. What is the expected value for distribution A? mu = 1 (Type an integer or decimal rounded to three decimal places as needed.) What is the expected value for distribution B? mu = 3 (Type an integer or decimal rounded to three decimal places as needed.) What is the standard deviation for distribution A? sigma = 1.175 (Type an integer or decimal rounded to three decimal places as needed.) What is the standard deviation for distribution B? sigma = (Type an integer or decimal rounded to three decimal places as needed.)

Explanation / Answer

a) E(X) = 1

b) E(X) = 3

c) E(X2) = 02 * 0.47 + 12 * 0.24 + 22 * 0.15 + 32 * 0.10 + 42 * 0.04

              = 2.38

Var(X) = E(X2) - (E(X))2

           = 2.38 - 12

           = 1.38

standard deviation = sqrt(1.38) = 1.175

d) E(X2) = 02 * 0.04 + 12 * 0.10 + 22 * 0.15 + 32 * 0.24 + 42 * 0.47

              = 10.38

Var(X) = E(X2) - (E(X))2

           = 10.38 - 32

           = 1.38

standard deviation = sqrt(1.38) = 1.175

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