Given the probability distributions shown to the right, complete the following p

Question

Given the probability distributions shown to the right, complete the following parts.

a. Compute the expected value for each distribution.

b. Compute the standard deviation for each distribution.

c. Compare the results of distributions A and B.

c. Use these results to compare distribution A and distribution B.

A.

Distribution A is symmetric, distribution B is

leftleft-skewed.

B.

Distribution A is

rightright-skewed,

distribution B is symmetric.

C.

Distribution A is symmetric, distribution B is symmetric.

D.

Distribution A is

leftleft-skewed,

distribution B is

rightright-skewed.

E.

Distribution A is

rightright-skewed,

distribution B is

leftleft-skewed.

Given the probability distributions shown to the right, complete the following parts.

a. Compute the expected value for each distribution.

b. Compute the standard deviation for each distribution.

c. Compare the results of distributions A and B.

Distribution A: X Distribution A: P(X) Distribution B: X Distribution B: P(X) 0 0.5 0 0.03 1 0.23 1 0.08 2 0.16 2 0.16 3 0.08 3 0.23 4 0.03 4 0.5

c. Use these results to compare distribution A and distribution B.

A.

Distribution A is symmetric, distribution B is

leftleft-skewed.

B.

Distribution A is

rightright-skewed,

distribution B is symmetric.

C.

Distribution A is symmetric, distribution B is symmetric.

D.

Distribution A is

leftleft-skewed,

distribution B is

rightright-skewed.

E.

Distribution A is

rightright-skewed,

distribution B is

leftleft-skewed.

Explanation / Answer

a. Expected Value of Distribution A = 0 * 0.5 + 1 * 0.23 + 2 * 0.16 + 3 * 0.08 + 4 * 0.03 = 0.91

Expected Value of Distribution B = 0 * 0.03 + 1 * 0.08 + 2 * 0.16 + 3 * 0.23 + 4 * 0.5 = 3.09

b. Variance of Distribution A = 0.5 * (0.91-0)2 +  0.23 * (0.91-1)2 +  0.16 * (0.91-2)2 +  0.08 * (0.91-3)2 +  0.03 * (0.91-4)2 = 1.2419

Standard deviation of Distribtuion A = sqrt (Variance) = 1.1144

Variance of Distribution A = 0.5 * (3.09 - 4)2 +  0.23 * ( 3.09-3)2 +  0.16 * (3.09 - 2)2 +  0.08 * (3.09 - 1)2 +  0.03 * (3.09 - 0)2 = 1.2419

Standard deviation of Distribtuion A = sqrt (Variance) = 1.1144

c. Here distribution A is Right Skewed and Distribution B is left skewed.

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