a. Suppose the lifetime X of a component, when measured in hours, has a gamma distribution with parameters α and β . Let Y = the lifetime measured in minutes. Derive the pdf of Y. [Hint: Y ≤ y iff X ≤ y / 60 . Use this to obtain the cdf of Y and then differentiate to obtain the pdf.]
b. If X has a gamma distribution with parameters and , what is the probability distribution of Y = cX?
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