6. Statistics and Probability
Expectation And Variance — Quiz
Test your understanding of expectation and variance with 5 practice questions.
Practice Questions
Question 1
A discrete random variable $X$ has the following probability distribution:
$$P(X=x) = \begin{cases} 0.1 & \text{for } x=0 \\ 0.3 & \text{for } x=1 \\ 0.4 & \text{for } x=2 \\ 0.2 & \text{for } x=3 \end{cases}$$
What is the expected value, $E(X)$?
$$P(X=x) = \begin{cases} 0.1 & \text{for } x=0 \\ 0.3 & \text{for } x=1 \\ 0.4 & \text{for } x=2 \\ 0.2 & \text{for } x=3 \end{cases}$$
What is the expected value, $E(X)$?
Question 2
If $X$ is a discrete random variable with $E(X) = 5$ and $Var(X) = 10$, what is the variance of $Y = 2X - 3$?
Question 3
A fair coin is tossed three times. Let $X$ be the number of heads obtained. What is the probability distribution for $X$?
Question 4
Given two independent discrete random variables $X$ and $Y$. If $E(X) = 4$, $Var(X) = 2$, $E(Y) = 6$, and $Var(Y) = 3$, what is $E(X+Y)$ and $Var(X+Y)$?
Question 5
A discrete random variable $X$ has $E(X) = 3$ and $E(X^2) = 12$. What is the variance of $X$?