6. Probability and Statistics

Discrete Distributions — Quiz

Test your understanding of discrete distributions with 5 practice questions.

Practice Questions

Question 1

A random variable $X$ follows a Binomial distribution with parameters $n$ and $p$. What is the standard deviation of $X$?

Question 2

In a Poisson distribution, if the mean number of events in an interval is $\lambda$, what is the probability of observing exactly $k$ events in that interval?

Question 3

A discrete random variable $X$ follows a Geometric distribution. What is the probability mass function (PMF) $P(X=k)$ for the number of trials until the first success, where $p$ is the probability of success on a single trial?

Question 4

If the probability of success in a Bernoulli trial is $p$, what is the variance of the Bernoulli distribution?

Question 5

A factory produces items, and the probability of a defective item is $0.02$. If items are inspected independently, what is the expected number of items to be inspected until the first defective item is found?