In this exercise, we shall prove that the three assumptions underlying the Poisson process model do indeed
Question:
a. For each positive integer n, divide the time interval into n disjoint subintervals of length t/n each. For i = 1, . . . , n, let Yi = 1 if exactly one arrival occurs in the ith subinterval, and let Ai be the event that two or more occurrences occur during the ith subinterval.
Let
For each nonnegative integer k, show that we can write Pr(X = k) = Pr(Wn = k) + Pr(B), where B is a subset of
b. Show that limn†’ˆž Pr(ˆªni=1Ai) = 0. Show that
c. Show that limn†’ˆž Pr(Wn = k) = eˆ’λ(λt)k/k!. limn†’ˆž n!/[nk(n ˆ’ k)!] = 1.
d. Show that X has the Poisson distribution with mean λt.
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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