PMF Geometric Distribution 3

Question 1

For a Geometric distribution (number of failures before first success), what is the PMF?

Accepted Answer

P(X=k) = (1-p)^k × p

Answer

When X counts failures before the first success, the PMF is P(X=k) = (1-p)^k × p for k = 0,1,2,…

Question 2

In the failures-before-success version of the Geometric distribution, what is E[X]?

Accepted Answer

(1-p)/p

Answer

When X counts failures before the first success, E[X] = (1-p)/p.

Question 3

A salesperson closes 20% of calls. Using the Geometric distribution, what is P(X=1) that the first call is a sale?

Accepted Answer

0.20

Answer

P(X=1) = (1-0.2)^0 × 0.2 = 1 × 0.2 = 0.20.

Question 4

A Geometric PMF decreases monotonically. What does this imply about most likely outcome?

Accepted Answer

The first trial (k=1) always has the highest probability of success

Answer

Since P(X=k) = (1-p)^(k-1) × p decreases as k increases, the most probable outcome is always k=1.

Question 5

Which formula gives P(X > k) for a Geometric distribution?

Accepted Answer

(1-p)^k

Answer

P(X > k) = (1-p)^k, the probability of k consecutive failures (no success in first k trials).

PMF - Probability Mass Function Practice Test