3. Probability Distributions

Discrete Distributions — Quiz

Test your understanding of discrete distributions with 5 practice questions.

Practice Questions

Question 1

A binomial distribution can be approximated by a Poisson distribution under certain conditions. Which of the following conditions is necessary for this approximation to be valid?

Question 2

Consider a scenario where a rare event occurs with a very low probability. If we are interested in the number of times this event occurs in a fixed interval of time or space, which discrete distribution would be most appropriate to model this situation?

Question 3

If a random variable $X$ follows a Geometric distribution with a probability of success $p$, what is the variance of $X$?

Question 4

A discrete random variable $X$ follows a Poisson distribution. If the probability of observing exactly one event is twice the probability of observing exactly two events, i.e., $P(X=1) = 2 \cdot P(X=2)$, what is the mean ($\lambda$) of the distribution?

Question 5

In a series of independent Bernoulli trials, what is the probability of observing the first success on the $k$-th trial, given that the probability of success on any single trial is $p$?