ECE302 Quiz-04

Question: What is the probability mass function (PMF) of a Geometric random variable X with parameter p?

• p_X​(k) = (1−p)^k−1 p^k

  for k=1,2,…k

• p_X​(k) = (1−p)^k−1 p

  for k=1,2,…k

• p_X​(k) = p(1−p)

• p_X​(k) = (1−p)^k

What does a Geometric random variable X∼Geometric(p) represent in the context of flipping a coin?

• The number of heads in a series of coin flips.

• The number of flips needed to get the first tail.

• The number of flips needed to get the first head.

• The probability of getting heads on each flip.

What is the expected value (mean) E[X] of a Geometric random variable X with parameter p?

• 1-p

• p

What is the probability mass function (PMF) of a Poisson random variable X with parameter λ

What is the mean and variance of a Poisson random variable X∼Poisson(λ)

• Mean = λ, Variance = λ²

• Mean = λ, Variance = λ

• Mean = λ², Variance = λ

• Mean = 1/λ, Variance = λ²

How does the Poisson distribution approximate the Binomial distribution?

• When the number of trials is small and probability is large.

• When the number of trials is large and probability is small.

• When the number of trials is small and probability is small.

• When the number of trials is large and probability is large.