Answer to Question #345335 in Statistics and Probability for Tomie

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