Question

A device has two components, A and B, that have independent failure times. The failure time for A, T₁, has density

while the failure time for B, T₂, has density

Let X be the last failure time. Find the variance of X, Var(X).

1. 0.02

2. 0.07

3. 0.10

4. 0.13

5. 0.18

Answer 1

Give values of X

0.02, 0.07, 0.1, 0.13, 0.18

Mean of X = Sum of Values of X / Number of Values of X

= (0.02 + 0.07 + 0.1 + 0.13 + 0.18) / 5

= 0.5/5

= 0.1

Variance = (x - )2 / n-1

We will calculate  (x - )2 as below in the table

X	X -	(X - )2
0.02	-0.08	0.0064
0.07	-0.03	0.0009
0.1	0	0
0.13	0.03	0.0009
0.18	0.08	0.0064
		(X - )2 = 0.0146

Varaince = (x - )2 / n-1

= 0.0146 / 5-1

= 0.0146 / 4

= 0.00365