Let $N$ have a $Bin(100, 1/4)$ distribution. Given $N=n$, flip a fair coin $n$ times, and let $X$ be the number of heads observed. What is the distribution of $X$ given $N=n$. Be sure to provide a range and a proper conditional probability mass function.
Can someone help with the intuition behind joint probability mass function. I feel it to has to be binomial, since the conditional will have two binomials over each other. Is it as simple as $$X|N=n\sim Bin(n,1/2)? $$