3. Statistics

Probability Basics — Quiz

Test your understanding of probability basics with 5 practice questions.

Practice Questions

Question 1

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is exactly 7?

Question 2

Let $X$ be a discrete random variable with the following probability mass function (pmf): $P(X=1)=0.2$, $P(X=2)=0.5$, $P(X=3)=0.3$. What is the expected value of $X$?

Question 3

Suppose $X$ is a continuous random variable with probability density function (pdf) $f(x) = 2x$ for $0 \leq x \leq 1$ and $f(x) = 0$ otherwise. What is the probability that $X$ is greater than 0.5?

Question 4

Consider two independent random variables $X$ and $Y$ with variances $\mathrm{Var}(X) = 4$ and $\mathrm{Var}(Y) = 9$. What is $\mathrm{Var}(2X - 3Y)$?

Question 5

A random variable $X$ follows a normal distribution with mean $\mu = 10$ and variance $\sigma^2 = 4$. What is the probability that $X$ is less than 8?