The number of failures of a computer system in a week of operation has the following pmf:

No of failures

Probability0123456

0.18

0.28

0.25

0.18

0.06

0.04

0.01

(a)Find the expected number of failures in a week.

(b)Find the variance of the number of failures in a week.

a. I'm not sure if i solved this correctly: 0.18 + 1(.28)+2(.25)+3(.18)+4(.06)+5(.04)+6(.01) = 2 failures?

b. (0-2)^2(.18)+ (1-2)^2(.28)+(2-2)^2(.25)+(3-2)^2(.18)+(4-2)^2(.06)+(5-2)^2(.04)+(6-2)^2(.01) = 1.94