In Example 6.14, Y1 and Y2 were independent exponentially distributed random variables
Chapter 6, Problem 6.63(choose chapter or problem)
In Example 6.14, Y1 and Y2 were independent exponentially distributed random variables, both with mean . We defined U1 = Y1/(Y1 + Y2) and U2 = Y1 + Y2 and determined the joint density of (U1, U2) to be fU1,U2 (u1, u2) = 1 2 u2eu2/ , 0 < u1 < 1, 0 < u2, 0, otherwise. a Show that U1 is uniformly distributed over the interval (0, 1). b Show that U2 has a gamma density with parameters = 2 and . c Establish that U1 and U2 are independent.
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