Free Probability Distributions MCQs with Answers

• A. Three
• B. Two
• C. Four
• D. One

Explanation: A normal distribution is determined by two parameters: its mean, which sets the centre, and its variance or standard deviation, which sets the spread.

• A. Continuous
• B. Constant
• C. Discrete
• D. Normal

Explanation: The normal distribution describes a continuous random variable, whose possible values form a continuous range and are represented by areas under the curve.

• A. One Outcome
• B. Two Outcome
• C. Three Outcome
• D. Four Outcome

Explanation: A binomial trial has exactly two mutually exclusive outcomes, conventionally called success and failure. The probabilities need not be equal, but the two-outcome structure is essential.

• A. Hypergeometric distribution
• B. Binomial distribution
• C. Poisson distribution
• D. Geometric distribution

Explanation: The hypergeometric distribution models sampling without replacement, so the probability changes from draw to draw. Binomial trials require independent trials with a constant success probability, which normally comes from replacement or a very large population.

• A. Independent
• B. Dependent
• C. Collectively Exhaustive
• D. None

Explanation: Hypergeometric trials are dependent because sampling is without replacement, so the outcome of one draw changes the probabilities on later draws. Independence is a defining condition of the binomial distribution instead.

• A. n is fixed
• B. Has two outcomes
• C. Trials are independent
• D. Probability of success varies from trial to trial

Explanation: A binomial distribution requires the success probability to remain constant on every trial. A changing probability is characteristic of sampling without replacement, commonly modeled by the hypergeometric distribution.

• A. 2
• B. 1
• C. 3
• D. 4
• E. No

Explanation: The standard hypergeometric distribution has three parameters: population size N, number of successes K, and sample size n. This differs from the binomial distribution, which is usually specified by n and p.

• A. P(X < 0)
• B. P(X = 0)
• C. P(X > 0)
• D. p(0 ≤ X≤ n)

Explanation: A binomial random variable can only take values from 0 through n, so values below zero are impossible and P(X < 0) = 0. Probabilities such as P(X = 0) and P(0 ≤ X ≤ n) are valid to calculate.

• A. npq
• B. np
• C. √npq
• D. √np
• E. nq-√

Explanation: A binomial variable is the sum of n Bernoulli trials, each having success probability p, so its expected value is np. The expression npq is the variance, not the mean.

• A. Binomial distribution
• B. Geometric distribution
• C. Sampling distribution
• D. Hypergeometrical distributionTry Statistical Software

Explanation: In hypergeometric sampling, items are drawn without replacement, so the composition of the remaining population changes and the success probability varies from trial to trial. Binomial trials instead require a constant success probability.