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If X has the Poisson pmf, how many different values can X be? O 10 O infinite O 2 6
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Answer #1

If X has the Poisson pmf then X can take infinitely many values.

X could be any integer starting from 0 to ∞

the pmf of X is as follows

X~Poisson(lambda)

e- p(z) =

where,   lambda > 0

and  x=0,1,2,...

X is the number of markers that pass out of three inspected is the definition of a random variable which has a Binomial distribution.

Here the probability that a marker passes when inspected is p

A Binomial random variable denotes the number of success in n trials of an experiment where probability of success at each trial is p.

X ~ Binomial(n,p)

the pmf of X :-

p(x)= inom{n}{x}p^{x}(1-p)^{n-x}

where

n=1,2,3,...

0leq pleq 1

x = 0,1,2,...,n

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