Free Probability Distributions MCQs with Answers

• A. All probability distribution
• B. The hypergeometric distribution
• C. The binomial distribution
• D. The Poisson distribution

Explanation: For a Poisson distribution with parameter λ, both the mean and variance equal λ.

• A. Poisson dist
• B. Standard dist
• C. Normal dist
• D. Hyper-geometric distribution

Explanation: With sufficiently large n and a suitable p, the binomial distribution is approximated by the normal distribution through the central limit…

• A. Become more positively skewed
• B. Become more negatively skewed
• C. Become symmetrical
• D. All of the above.

Explanation: The binomial skewness is determined by q − p: at p = 0.50 it is symmetric, but as p falls below 0.50, q becomes larger and the…

• A. 6
• B. 1
• C. 2/5
• D. None of these

Explanation: The mean of a binomial distribution is np. Thus, np = 10 × 3/5 = 6.

• A. Probability remains constant for all the trials.
• B. Probability changes from trial to trial
• C. Successive trial are dependent
• D. Both (b) & (c) but not (a)

Explanation: In a hypergeometric distribution, sampling is without replacement, so the success probability changes after each draw and successive…

• A. P > q
• B. P = 1/2
• C. Probability of success & probability of failure are equal
• D. Both (b) & (c) but not (a)

Explanation: A binomial distribution is symmetric when the success and failure probabilities are equal, so p = q = 1/2.

• A. X
• B. n x p
• C. n(1 - 1)
• D. ∑fx/∑f

Explanation: For a binomial distribution with n trials and success probability p, the expected number of successes is np.

• A. {nx}px qn-x
• B. {nx}px(1 - P)x-n
• C. nCxpnqnx
• D. {nx}p(1 - P)x

Explanation: The binomial probability for exactly x successes is C(n,x)p^xq^(n−x), where q = 1 − p.

• A. n, q
• B. n, p, q
• C. q, p
• D. n, p

Explanation: A binomial distribution has two independent parameters: n, the fixed number of trials, and p, the probability of success.

• A. Times
• B. Fixed
• C. Expansion
• D. Trial

Explanation: A defining condition of the binomial experiment is that it is repeated a fixed number n of times.

• A. 60
• B. 30
• C. 20
• D. 40

Explanation: The binomial mean is np, so the mean is 400 × 0.1 = 40. This makes option (d) correct.

• A. 1 to n
• B. 0 to n
• C. 1 to ∞
• D. 0 to ∞

Explanation: For a binomial variable, the number of successes can be as low as 0 and as high as all n trials, so its range is 0 to n.

• A. p > q
• B. P = q
• C. p < q
• D. P/q

Explanation: A binomial distribution is positively skewed when successes are less likely than failures, meaning p<q.

• A. n; fixed number of times
• B. a large number times
• C. n; where n < 0
• D. n = 100

Explanation: A binomial experiment consists of n independent trials, where n is a fixed positive integer.

• A. Dependent
• B. Independent
• C. Linear
• D. Equal

Explanation: The formulas mean=np and variance=npq apply when the n Bernoulli trials are independent and have the same success probability p.

• A. Pq
• B. nP
• C. xm
• D. Non of these

Explanation: The binomial mean equals the expected number of successes, calculated as the number of trials multiplied by the success probability…

• A. Equal to variance
• B. Less than variance
• C. Greater than varince
• D. None of these

Explanation: The binomial mean is np and its variance is npq. Since 0<q<1 in the standard case, np is greater than npq, so the mean is greater than the…

• A. 4
• B. 3
• C. 2
• D. 6

Explanation: A binomial distribution is determined by two parameters: n, the number of trials, and p, the probability of success on each trial.

• A. Dependent
• B. Independent
• C. Equally Likely
• D. Mutually exclusive
• E. Non

Explanation: The trials in a binomial experiment are independent, meaning the outcome of one trial does not change the probability of success on…

• A. 10
• B. 12
• C. 2.1
• D. 21
• E. None

Explanation: For a binomial variable, variance is npq, where q = 1 - p. Here, npq = 10(0.3)(0.7) = 2.1.