PMF Geometric Distribution

Question 1

What does the Geometric distribution model?

Accepted Answer

The number of trials until the first success

Answer

The total number of successes in n trials

Answer

The number of failures before the k-th success

Answer

The time between two Poisson events

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

P(X=k) = p^k × (1-p)

Answer

P(X=k) = p^(k-1) × (1-p)

Answer

P(X=k) = k × p × (1-p)^k

Question 3

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

Accepted Answer

1/p

Answer

p

Answer

1/(1-p)

Answer

(1-p)/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

0.4

Answer

4

Answer

1.6

Question 5

Which property makes the Geometric distribution unique among discrete distributions?

Accepted Answer

Memoryless property

Answer

Symmetry around the mean

Answer

Both mean and variance equal λ

Answer

Sum of two Geometric variables is Geometric

Question 6

What is the variance of a Geometric distribution with parameter p?

Accepted Answer

(1-p)/p²

Answer

1/p

Answer

p/(1-p)

Answer

(1-p)/p