Question

X | 0 | 2 | 5 | 7 | 9

P(X) |0.1|0.2|0.3|0.2|0.2

1. What is the mean of the probability distribution?

a. 5.1

b. 5.5

c. 6.0

d. 4.0

2. What is the variance of the probability distribution?

a. 18.15

b. 2.26

c. 8.29

d. 2.88

Answer 1

1.

$$mean=E(X)=0.1(0)+0.2(2)+0.3(5)$$

$$+0.2(7)+0.2(9)=5.1$$

a. 5.1

2.

$$E(X^2)=0.1(0)^2+0.2(2)^2+0.3(5)^2$$

$$+0.2(7)^2+0.2(9)^2=34.3$$

$$Var(X)=\sigma^2=E(X^2)-(E(X))^2$$

$$=34.3-(5.1)^2=8.29$$

c. 8.29