Question

Find P(X≤0) if the random variable X has a Poisson distribution such that P(X=1)=P(X=2).

Find P(X≤0) if the random variable X has a Poisson distribution such that P(X=1)=P(X=2).

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Answer #1

Let , X has Poisson distribution with parameter 'm'

Therefore , the probability mass function of X is ,

; x=0,1,2,........

= 0 ; otherwise

Since , P(X=1) = P(X=2)

Therefore , the X has Poisson distribution with parameter m=2.

Now , we wan to find the

Therefore ,  

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