# Question: The lifetime in months of a certain part has a

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?

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