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1. Let X1, X2, ... be a sequence of i.i.d. Exp(1). Define Sn = X1 + X2 + ... + Xn. (a) Find the probability

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1. Let X1, X2, ... be a sequence of i.i.d. Exp(1). Define Sn = X1 + X2 + ... + Xn. (a) Find the probability density function of Sn. (5 pt) (b) Fix > > 0. Define the random variable N as N = min {n : X1 + X2 + ... + Xn+1 > >}. Find the probability mass function of N. (10 pt)

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