1. ## Expectation

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. (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

2. 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. (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
I haven't checked the arithmetic but the approach is OK.