Problem 18E

The lifetime in months of a certain part has a gamma distribution with α = θ = 2. A company buys three such parts and uses one until it fails, replacing it with a second part. When the latter fails, it is replaced by the third part.What are the mean and the variance of the total lifetime (the sum of the lifetimes of the three parts) associated with this situation?

Step 1 of 4

Given

Gamma distribution of

Let us assume that the three bought parts are independent Each of these parts has the distribution of