independent, Let W1 be the each weight with of the pdf ith airline passenger's luggage. Assume that the weights are
and zero otherwise.
(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,
(c) If Wa: is the largest value out of n, then show that W. F Basn
(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?
Question 4) [5 marks) Suppose that N has a Poisson distribution with probability mass function
for n = 0,1,2,
(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)
and N has the above Poisson distribution.
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