1. Probability Theory

Continuous Distributions — Quiz

Test your understanding of continuous distributions with 5 practice questions.

Practice Questions

Question 1

An insurance company models the time until a claim is filed, $T$, using an Exponential distribution with a mean of $8$ years. What is the probability that a claim is filed between $4$ and $12$ years?

Question 2

A random variable $X$ follows a Gamma distribution with shape parameter $\alpha = 4$ and scale parameter $\theta = 3$. What is the variance of $X$?

Question 3

If $X$ is a continuous random variable with a probability density function (PDF) $f(x)$, and a new random variable $Y$ is defined as $Y = g(X)$, what is the general formula for the PDF of $Y$, denoted as $f_Y(y)$, assuming $g(X)$ is a monotonic function?

Question 4

A financial analyst models the daily returns of a stock using a Normal distribution with a mean of $0.002$ and a standard deviation of $0.03$. What is the probability that the daily return is negative?

Question 5

Which of the following statements about the memoryless property of the Exponential distribution is true?