Answer to Question #333806 in Statistics and Probability for Khay

Question

Suppose that the life span in months of a lead bulb is a random variable and let Y1 and Y2 denote

the life span of two different types of lead bulbs produced by different companies. If Y1 and Y2 are

independent exponentially distributed random variables, both with mean β and let X1 =

Y1

Y1 + Y2

and

X2 = Y1 + Y2. Find and identify the marginal distributions of X1 and X2.