Review: Joint, Conditional, and Marginal Distributions: Discrete Example
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?
Lower limit of Y given X = x:
Upper limit of Y given X = x:
Is E[Y | X = x] a linear function of x?
Yes
No
What is E[Y]?
Hint: Use the tower property of expectation (law of iterated expectation).