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Independent Variables

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Let X1 and X2 be two independent random variables having Poisson Dist. with parameters mew(subscript1)=2 and mew(subscript 2)=3 respectively. Then the marginal distribution for the random variable X2 is :

a.) h(X2) = e^-2*2^Xz/X2!, x2=0,1,2,3,...

b.) h(X2) = e^-5*5^Xz/X2!, x2=0,1,2,3,...

c.) h(X2) = e^-3*3^Xz/X2!, x2=0,1,2,3,...

d.) h(X2) = e^-3*3^Xz/X2!, x2=1,2,3,...

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Solution Summary

Let X1 and X2 be two independent random variables having Poisson Dist. with parameters mew(subscript1)=2 and mew(subscript 2)=3 respectively. Then the marginal distribution for the random variable X2 is :

a.) h(X2) = e^-2*2^Xz/X2!, x2=0,1,2,3,...

b.) h(X2) = e^-5*5^Xz/X2!, x2=0,1,2,3,...

c.) h(X2) = e^-3*3^Xz/X2!, x2=0,1,2,3,...

d.) h(X2) = e^-3*3^Xz/X2!, x2=1,2,3,...

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Answer (c):

Because, marginal distribution of X2
f(X2) = integration (- ...

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