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

P(X=k) = (1-p)^(k-1) × p

Answer

P(X=k) = p^k × (1-p)

Answer

P(X=k) = C(k,1) × p × (1-p)^k

Question 2

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

Accepted Answer

(1-p)/p

Answer

1/p

Answer

p/(1-p)

Answer

1/(1-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

0.80

Answer

0.16

Answer

0.04

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

Large k values have higher probability

Answer

The median equals the mean

Answer

All outcomes are equally likely

Question 5

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

Accepted Answer

(1-p)^k

Answer

1 - (1-p)^k

Answer

p^k

Answer

1 - p^k

Question 6

How does the Geometric distribution relate to the Negative Binomial distribution?

Accepted Answer

The Geometric distribution is a special case of the Negative Binomial with r=1

Answer

The Negative Binomial is a special case of the Geometric

Answer

They are identical distributions

Answer

There is no relationship between them