Quiz on Common Discrete Distributions

What is a parametric family in statistics?

• A collection of random variables

• A family of distributions with no parameters

• A single distribution with fixed parameters

• A collection of distributions described by parameters

What does the mean of a Bernoulli distribution represent?

• The total number of trials

• The probability of success

• The variance of the distribution

• The cumulative probability

In a binomial distribution, what does the parameter 'n' represent?

• The variance of the distribution

• The probability of success

• The number of trials

• The mean of the distribution

What is the probability mass function (p.m.f.) of a binomial distribution?

• f(x) = (n choose x) p^x (1-p)^(n-x)

• f(x) = p(1-p)^(x-1)

• f(x) = p^x

• f(x) = (1-p)^x

What is the variance of a binomial distribution?

• np(1-p)

• np

• n(1-p)

• p(1-p)

What does the negative binomial distribution count?

• The number of trials until a fixed number of successes

• The number of successes in a fixed number of trials

• The total number of failures

• The average number of successes

What is the mean of a geometric distribution?

• p/(1-p)

• 1/(1-p)

• 1/p

• p

Which distribution is known for its 'memoryless' property?

• Bernoulli distribution

• Negative binomial distribution

• Binomial distribution

• Geometric distribution

In the context of the Bernoulli distribution, what does 'p' represent?

• The variance of the distribution

• The probability of success

• The total number of trials

• The mean of the distribution

What is the formula for the cumulative distribution function (c.d.f.) of a binomial distribution?

• F(x) = p^x

• F(x) = sum from i=0 to x of (n choose i) p^i (1-p)^(n-i)

• F(x) = 1 - (1-p)^x

• F(x) = (1-p)^x