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
Asked Jun 4, 2019

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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Expert Answer

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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