Question: 1. Consider the probability space (R+, B(R+), P) , where R+ = (0, 00) and P is the Gamma(2, 3) distribution, dP(x) = gxe-3 dx.

1. Consider the probability space (R+, B(R+), P) , where R+ = (0, 00) and P is the Gamma(2, 3) distribution, dP(x) = gxe-3 dx. Consider the random variables n +1 n+1 fn(20) = , TERA, nEN. n2 exp n Using the dominated convergence theorem, prove that the limit lim E(fn) exists and find it. [9 Marks]

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