PMF Geometric Distribution

Question 1

What does the Geometric distribution model?

Accepted Answer

The number of trials until the first success

Answer

The Geometric distribution models the number of independent Bernoulli trials needed to achieve the first success.

Question 2

What is the PMF of the Geometric distribution (number of trials until first success)?

Accepted Answer

P(X=k) = (1-p)^(k-1) × p

Answer

The Geometric PMF P(X=k) = (1-p)^(k-1) × p represents k-1 failures followed by one success.

Question 3

What is the mean (expected value) of a Geometric distribution with success probability p?

Accepted Answer

1/p

Answer

The expected number of trials until the first success is E[X] = 1/p.

Question 4

A basketball player has a 40% free throw success rate. What is the expected number of throws to make the first basket?

Accepted Answer

2.5

Answer

E[X] = 1/p = 1/0.4 = 2.5 throws expected until the first success.

Question 5

Which property makes the Geometric distribution unique among discrete distributions?

Accepted Answer

Memoryless property

Answer

The Geometric distribution is the only discrete distribution with the memoryless property: past failures do not affect future probabilities.

PMF - Probability Mass Function Practice Test