Let X,. X,... be a sequence of independent identically distributedRVs having common MGF M(0), and let N be an RV taking non-negative integervalues with PGF $(s); assume that N is independent of the sequence (X,). Show thatZ = X, + X; +...+ X, has MGF 4(M(0)).The sizes of claims made against an insurance company form an independent identicallydistributed sequence having common PDF f(x)=e-'.x>0. The number of claims duringa given year had the Poisson distribution with parameter A. Show that the MGF of thetotal amount T of claims during the year is(0) = exp{A0/(1 – 0)} for 0 < 1.Deduce that T has mean and variance 2A.

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Answered: Let X. X,.... be a sequence of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. For a fully discrete whole life insurance of 1 issued to (45) with annual level premiums, you are given: Find 25V. t V 22 0.235 23 0.255 24 0.272 P45+t 0.985 0.980 0.975
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Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.75, Pr(B) = 0.55, Pr(C) = 0.25. 1. Find Pr(A'), Pr(B'), and Pr(C'). Pr(A') = Pr(B') = %3D Pr(C') = 2. If Pr(A U B) = 0.75., find Pr(A n B). Pr(A n B) = 3. Suppose that we know that B and C are disjoint events. Find Pr[B U C]. Pr[B U C] = 4. Suppose that instead of being disjoint C C B. Find Pr[B U C]. Pr[BU C] =
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6. The amount of a loss X follows the uniform distribution on [0, 100]. An insurance policy on this loss has an ordinary deductible of 10, a maximum amount paid of 50, and a coinsurance of 80%, which is applied after the deductible. After losses are subject to inflation of 10%, calculate the expected claim amount paid per loss on this policy.

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