Question

Let 𝑋 be a discrete Poisson random variable with parameter 𝜆. Given 𝑋=𝑥, let 𝑌 be the binomial random variable 𝖡𝗂𝗇𝗈𝗆(𝑥,𝑝), where 𝑝 is the binomial parameter.

Given 𝑋=𝑥, what are the values that 𝑌 can take?

Answer 1

Given that 𝑋=𝑥, the possible values that 𝑌 can take on will depend on the value of 𝑥.

For 𝑌 to be a binomial random variable with 𝑥 trials, 𝑌 can take on any value from 0 to 𝑥, inclusively.

Therefore, the values that 𝑌 can take on are {0, 1, 2, ..., 𝑥}.