This week the number X of claims coming into aninsurance office is Poisson with mean 100. Theprobability that any particular claim relates toautomobile insurance is .6, independent of anyother claim. If Y is the number of automobileclaims, then Y is binomial with X trials, eachwith "success" probability .6.a. Determine E(YIX = x) and V(YIX = x).b. Use part (a) to find E(Y).c. Use part (a) to find V(Y).

X follows a Poisson distribution with a mean of 100 E(x)=λ=100 X~P(λ) and Y|X follows a binomial distribution with a success probability of 0.6 p=0.6 Y|X=x~Bin(n,p) Y|X=x~Bin(x,0.6)a) here we have tind E(Y|X=x) and V(Y|X=x) E(Y|X=x)=n×p=0.6×x V(Y|X=x)=n×p×(1-p) =0.6×(1-0.6)×x =0.6×0.4×x =0.24×x b)now we have to find E(Y) E(Y)=E(E(Y|X=x)) =E(0.6×x)=0.6×E(x)=0.6×100=60 c)now to calculate V(Y) V(Y)=EVY|X=x+VEY|X=x=E0.24×x+V0.6×x=0.24×Ex+0.36×Vx=0.24×100+0.36×100=24+36=60

Math

Statistics

This week the number X of claims coming ir nsurance office is Poisson with mean 100 probability that any particular claim relat utomobile insurance is .6, independent o other claim. If Y is the number of autom laims, then Y is binomial with X trials, vith "success" probability .6. . Determine E(YIX = x) and V(YIX = x). . Use part (a) to find E(Y). . Use part (a) to find V(Y).

This week the number X of claims coming ir nsurance office is Poisson with mean 100 probability that any particular claim relat utomobile insurance is .6, independent o other claim. If Y is the number of autom laims, then Y is binomial with X trials, vith "success" probability .6. . Determine E(YIX = x) and V(YIX = x). . Use part (a) to find E(Y). . Use part (a) to find V(Y).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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This week the number X of claims coming into an
insurance office is Poisson with mean 100. The
probability that any particular claim relates to
automobile insurance is .6, independent of any
other claim. If Y is the number of automobile
claims, then Y is binomial with X trials, each
with "success" probability .6.
a. Determine E(YIX = x) and V(YIX = x).
b. Use part (a) to find E(Y).
c. Use part (a) to find V(Y).

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