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7.6.3. 15, independent, Let W1 be the each weight with of the pdf ith airline passenger's luggage. Assume that the weights are irocw<b and zero otherwise. 100 (a) For n - 100, 0 = 3, and B - 80, approximate P (b) If WI: is the smallest value out of n, then show that W, co. (c) If Wa: is the largest value out of n, then show that W. F Basn 80. (d) Find the limiting distribution of (e) Find the asymptotic normal distribution of the median, where k/n 0.5 with k - 0.5n bounded. (f) To what does We: of (e) converge stochastically? (g) What is the limiting distribution of n¹/°W1../B? </b Question 4) [5 marks) Suppose that N has a Poisson distribution with probability mass function (pmf) ((n)=ector for n = 0,1,2, n! (1] (a) Find the probability generating function (pgf)of N, Gs(s)=E(s*). Suppose Y = X1 + X2 + X3 + XN where the X, are independently, identically distributed random varaiables, all with moment generating function (mgf) 1 , and N has the above Poisson distribution.

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