5. Statistics

Continuous Distributions — Quiz

Test your understanding of continuous distributions with 5 practice questions.

Practice Questions

Question 1

For a random variable $X\sim N(5,4)$, calculate the probability $P(3< X <7)$.

Question 2

Let $X\sim \mathrm{Exp}(\lambda)$ and define $Y=X^{2}$. What is the probability density function of $Y$ for $y>0$?

Question 3

If $X_{1}$ and $X_{2}$ are independent $\mathrm{Exp}(\lambda)$ random variables, the sum $Z=X_{1}+X_{2}$ has which probability density function?

Question 4

Let $X\sim N(0,1)$ and define $Y=|X|$. What is the probability density function of $Y$ for $y\ge0$?

Question 5

For $X\sim U(0,10)$, what is the conditional expectation $E[X\mid X>7]$?