Question: 6.17. If X is a random variable having an exponential distribution with the parameter 0, use Theorems 4.10 on page 128 and 6.4 to find

6.17. If X is a random variable having an exponential distribution with the parameter 0, use Theorems 4.10 on page 128 and 6.4 to find the moment-generating function of the random variable Y = X -0.THEOREM 4.10. If a and b are constants, then 1. MXta(t) = Ele(X+a)t] = eat . Mx(t); 2. Mbx(t) = E(ebXt) = Mx(bt); Xta 3. MXta (t) = Ele ")'1 = ebt . MXTHEOREM 6.4. The moment-generating function of the gamma distribution is given by Mx(t) = (1- Bt)

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