1) Consider a random sample X₁, X2, ..., Xn from a population distributed with the following mass function: f(x) = 3xe-3 x! 0, for x = 0,1,...,00 elsewhere a) What is the mean and variance of a statistic Y = Σ₁X₁? 10 Li=X? 10 1 10 b) What is the mean of the statistic Y = [²º₁X? c) Find the probability distribution function of Y = Zi=1 d) What is the probability that Y = ₁X₁ is at least 3? 10 1₁X₁. i=1

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