
Expectation
The number of failures of a computer system in a week of operation has the following pmf:
No of failures Probability 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. (02)^2(.18)+ (12)^2(.28)+(22)^2(.25)+(32)^2(.18)+(42)^2(.06)+(52)^2(.04)+(62)^2(.01) = 1.94

Quote:
Originally Posted by
aaronrj The number of failures of a computer system in a week of operation has the following pmf: No of failures 0
1
2
3
4
5
6
Probability 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. (02)^2(.18)+ (12)^2(.28)+(22)^2(.25)+(32)^2(.18)+(42)^2(.06)+(52)^2(.04)+(62)^2(.01) = 1.94
I haven't checked the arithmetic but the approach is OK.