PMF Negative Binomial Distribution

Question 1

What does the Negative Binomial distribution model?

Accepted Answer

The number of trials needed to achieve r successes

Answer

The number of successes in n trials

Answer

The time until the first event

Answer

The count of events per unit time

Question 2

What is the PMF of the Negative Binomial (number of failures before r-th success)?

Accepted Answer

P(X=k) = C(r+k-1, k) × p^r × (1-p)^k

Answer

P(X=k) = C(n,k) × p^k × (1-p)^(n-k)

Answer

P(X=k) = C(k-1,r-1) × p^r × (1-p)^(k-r)

Answer

P(X=k) = (1-p)^(k-1) × p

Question 3

What is the mean of a Negative Binomial distribution (failures before r-th success)?

Accepted Answer

r(1-p)/p

Answer

r/p

Answer

rp

Answer

r(1-p)

Question 4

Which special case of the Negative Binomial gives the Geometric distribution?

Accepted Answer

r = 1

Answer

r = 0

Answer

p = 0.5

Answer

r = n

Question 5

An inspector needs to find 3 defective items. Each item has a 20% chance of being defective. What distribution models the number of items inspected until the 3rd defect?

Accepted Answer

Negative Binomial with r=3, p=0.2

Answer

Binomial with n=3, p=0.2

Answer

Poisson with λ=0.6

Answer

Geometric with p=0.2

Question 6

What is the variance of the Negative Binomial distribution (failures before r-th success)?

Accepted Answer

r(1-p)/p²

Answer

r(1-p)/p

Answer

r/p²

Answer

rp(1-p)