1. Probability Theory

Discrete Distributions — Quiz

Test your understanding of discrete distributions with 5 practice questions.

Practice Questions

Question 1

Which of the following distributions is most appropriate for modeling the number of policyholders who make a claim in a year, given that each policyholder's claim is an independent Bernoulli trial with a fixed probability of success?

Question 2

An insurance company observes that the number of major accidents in a city follows a Poisson distribution with an average rate of $1.5$ accidents per month. What is the probability that there will be exactly 2 major accidents in the next month?

Question 3

A new actuary is studying the probability of an individual passing their first actuarial exam. If the probability of passing is $p$, and each attempt is independent, which distribution models the number of attempts until the actuary passes their first exam?

Question 4

For a Bernoulli random variable $X$ with probability of success $p$, what is the expected value $E[X]$ and variance $Var(X)$?

Question 5

In a Binomial distribution with parameters $n$ (number of trials) and $p$ (probability of success), what is the probability of getting at least one success?