(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X is distributed exponentially with λa=2. Y is distributed exponentially with λb = 3. X and Y are independent.

Let W=max(X,Y), the time until both persons catch their first fish. Let k be a positive integer. Find E(W^k).

Also, find P{(1/3)<X/(X+Y)<(1/2)}

2. Relevant equations

f(X) = λa e^(-λa x)

f(Y) = λb e^(-λb y)

f(X,Y) = f(X)f(Y)

Mx(t) = E(e^t)

Mx^k(0)=E(W^k)

3. The attempt at a solution

I found f(w)=3e^(-3w)+2e^(-2w)-5e^(-2w-3w) but not sure where to go from here

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# Homework Help: Moment Generating Function Given pdf

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