Quiz on Discrete Distribution

If X ~ Binomial(n, p), what is the mean of X?

• p

• np(1−p)

• np

• n

The variance of a discrete uniform distribution on the integers {1, 2, ..., n} is

Which of the following distributions has the property that its mean and variance are equal?

• Uniform

• Binomial

• Poisson

• Geometric

If X ~ Negative Binomial(r, p), what does the random variable X represent?

• The number of trials required to get the first success.

• The number of successes in a sample drawn without replacement.

• The number of successes in a fixed number of trials.

• Binomial(5, 0.6)

• Binomial(5, 0.4)

• Bernoulli(0.6)

• Poisson(0.6)

1.       If X ~ Poisson(λ) and Y ~ Poisson(μ) are independent, what is the conditional distribution of X given X + Y = n?

• Poisson(λ)

• Hypergeometric(n,λ,λ+μ)

• Binomial(n,λ)

Which of the following distributions is a special case of the negative binomial distribution?

• Binomial

• Geometric

• Poisson

• Uniform

What is the probability generating function (PGF) of a degenerate distribution at a constant 'c'?

• s

• 1

The hypergeometric distribution is used for sampling...

• ...where the number of trials is not fixed.

• ...with replacement from a finite population.

• ...without replacement from a finite population.

• ...from an infinite population.