Question

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

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()

where,   

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 :-

where

n=1,2,3,...

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