Common Distributions

What is the key parameter of the Bernoulli distribution?

• The variance of the distribution
• The mean of the distribution
• Number of trials

• The probability of success (p)

What is the relationship between the mean and variance of a Poisson distribution?

• The mean is half the variance.
• The mean and variance of a Poisson distribution are equal.
• The variance is always zero.
• The mean is twice the variance.

For a normal distribution X∼N(μ,σ^2), what transformation standardizes X?

• Z = (X * σ) + μ
• Z = (X - σ) / μ
• Z = (X - μ) / σ
• Z = (X + μ) / σ

What is the support of the exponential distribution?

• R+

• [1, 2]
• R

• [-1,1]

What is the defining property of the logistic distribution?

• It is skewed to the right.

• The defining property of the logistic distribution is its uniform probability density function.

• It has no closed-form cumulative distribution function (CDF).

• It has a bell shape similar to the normal distribution.

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

• Geometric distribution
• Uniform distribution
• Exponential distribution
• Poisson distribution

The parameter λ in the exponential distribution represents:

• The scale parameter

• The location parameter

• The rate parameter

• The skewness

Which of the following describes a use case for the hypergeometric distribution?

• Modeling the time until the first success in a sequence of trials

• Modeling the number of successes in sampling without replacement

• Calculating probabilities for a normal distribution.
• Estimating parameters of a binomial distribution.

A Poisson distribution is often used to model:

• The average of a set of data points.
• The probability of a single event occurring.
• The distribution of continuous random variables.
• The number of events occurring in a fixed interval of time or space.

Fill in the Blank Question:

The ___________ distribution models the number of successes in a fixed number of independent trials, where each trial has the same probability of success, denoted by p.