PMF Geometric Distribution 2

Question 1

For a Geometric distribution with p = 0.25, what is P(X = 3)?

Accepted Answer

(0.75)² × 0.25 ≈ 0.141

Answer

(0.25)² × 0.75 ≈ 0.047

Answer

0.75 × 0.25 ≈ 0.188

Answer

(0.25)³ ≈ 0.016

Question 2

What is the support of the Geometric distribution (number-of-trials version)?

Accepted Answer

{1, 2, 3, 4, …}

Answer

{0, 1, 2, 3, …}

Answer

{1, 2, …, n}

Answer

{0, 1}

Question 3

Using the memoryless property, if X ~ Geometric(p=0.3) and you have already failed 5 times, what is the probability the next trial succeeds?

Accepted Answer

0.3

Answer

0.7

Answer

0.3 × (0.7)^5

Answer

1 - (0.7)^5

Question 4

How does increasing p affect the Geometric PMF?

Accepted Answer

The distribution becomes more concentrated near k=1

Answer

The distribution becomes more spread out

Answer

The mean increases

Answer

The variance increases

Question 5

What is the CDF of the Geometric distribution, P(X ≤ k)?

Accepted Answer

1 - (1-p)^k

Answer

(1-p)^k

Answer

1 - p^k

Answer

p^k

Question 6

Which scenario is best modeled by a Geometric distribution?

Accepted Answer

Rolling a die until getting a 6

Answer

Counting the number of 6s in 10 rolls

Answer

Time between two bus arrivals

Answer

Number of heads in 20 coin flips