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4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass function prob- 1 (log 3) P
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a ELN) og) (oa s) ogs) Cags 20 ら109 3、× log3 og 3 00 3) gs 1 (N) EN(N-1 ELN)-EN og s-log 3) og -1g3-g) PM-265 NAMt26) Rl1625

Cov((T,N)=E(TN)-E(T)E(N)=E{NE(T|N)}-E(T)E(N)=E(N*700N)-1153.53*1.6479

=700*{V(N)+E2(N)}-1153.53*1.6479

=700*(.7427+1.6479*1.6479)-1153.53*1.6479=519.89

corr(T,N)=519.89/[SD(T)SD(N)]=519.89/square root of (561671*.7427)= 0.8049404

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