3. Discrete Random Variables

Random Variables — Quiz

Test your understanding of random variables with 5 practice questions.

Practice Questions

Question 1

For a discrete random variable $X$ with probability mass function $p(x)$ and any function $g(x)$, which formula gives the expectation $E[g(X)]$?

Question 2

Given the discrete random variable $X$ with PMF $p(1)=0.1$, $p(2)=0.4$, and $p(3)=0.5$, what is $E[X^2]$?

Question 3

Let $X$ be a discrete random variable taking values $\{1,2,3,4\}$ each with probability $0.25$. Define $Y=2X+1$. Which of the following gives the PMF of $Y$?

Question 4

Suppose $X$ is the number of heads in three independent fair coin flips. What is $P(X=2)$?

Question 5

For a discrete random variable $X$ with cumulative distribution function $F(x)$, what is the size of the jump of $F(x)$ at $x=k$?