Discrete Mathematics
# Discrete Random Variables

Today, Joe's class took a math quiz consisting of two problems. For a randomly selected student, let $X$ be the points earned on the first question and $Y$ be the points earned on the second question. The joint probability distribution of $X$ and $Y$ is given in the following table:

$\begin{matrix} & X=0 & X=5 & X=10 & X=15 \\ Y=0 & 0.05 & 0.05 & 0 & 0.07 \\ Y=5 & 0 & 0 & 0.18 & 0.07 \\ Y=10 & 0 & 0.11 & 0.36 & 0.11 \end{matrix}$

What is the expected points that a randomly selected student got?

Today, Joe's class took a math quiz consisting of two problems. For a randomly selected student, let $X$ be the points earned on the first question and $Y$ be the points earned on the second question. The joint probability distribution of $X$ and $Y$ is given in the following table:

$\begin{matrix} & X=0 & X=5 & X=10 & X=15 \\ Y=0 & 0.07 & 0.07 & 0 & 0.07 \\ Y=5 & 0 & 0 & 0.18 & 0.07 \\ Y=10 & 0 & 0.11 & 0.32 & 0.11 \end{matrix}$

The students who have earned a total of less than $15$ points will be taking a makeup test. What is the probability that a randomly chosen student will be taking a makeup test?