Question $(1)$ A fair dice is thrown. Let $\text{X}$ denotes number of factors of the number on the upper face. Find probability distribution of $\text{X}$
$\begin{array}{|c| |c| |c|}\hline x & 1 & 2 & 3 & 4 \\ \hline P(x) & \dfrac{1}{6} & \dfrac{3}{6} & \dfrac{1}{6} & \dfrac{1}{6} \\ \hline\end{array}$
I want to know that can we write probability mass function and cumulative distribution function for the above experiment.? If yes, then How?
Question $(2)$ Two cards are randomly drawn, with replacement, from a well shuffled deck of $52$ playing cards. Find the probability distribution of the number of aces drawn.
Probability distribution of above experiment is
$\begin{array}{|c| |c| |c|}\hline x & 0 & 1 & 2 \\ \hline P(x) & \dfrac{144}{169} & \dfrac{24}{169} & \dfrac{1}{169} \\ \hline\end{array}$
and It's probability mass function is given by $f(x)={4 \choose x}\bigg(\dfrac{1}{13}\bigg)^x \bigg(\dfrac{12}{13}\bigg)^{2-x}$
My Doubt: Can we write Probability mass function and cumulative distribution function for question number $(1)$