# the following probability distribution represents the number of people living in a household (x), and the probability of occurrence (p(x). compute the expected value (mean), the variance, and standard deviation for the random variable. calculations for the mean.x 1 2 3 4 5p(x) .33 .29 .27 .07 .04

Question

the following probability distribution represents the number of people living in a household (x), and the probability of occurrence (p(x). compute the expected value (mean), the variance, and standard deviation for the random variable. calculations for the mean.
x 1 2 3 4 5
p(x) .33 .29 .27 .07 .04

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Step 1

Given the value of X (households) = 1, 2, 3, 4, and 5.

Probability of occurrence Px = 0.33, 0.29, 0.27, 0.07, and 0.07

Step 2
 X PX x*Px x2 x2px 1 0.33 0.33 1 0.33 2 0.29 0.58 4 1.16 3 0.27 0.81 9 2.43 4 0.07 0.28 16 1.12 5 0.04 0.2 25 1 Expected value E(x)= 2.2 ∑ x2 * Px = 6.04
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