Free Probability Distributions MCQs with Answers
132 Probability Distributions MCQs from Statistics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
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132 questions · page 7 of 14
61. The mean and the variance are equal in________________?
- 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. The binomial variance is npq, which generally differs from its mean np.
Correct answer: The Poisson distribution62. When 'n' becomes very large, binomial distribution tends to ______________?
- 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 theorem. A Poisson approximation requires the additional condition that p is small while np remains fixed.
Correct answer: Normal dist63. For a binomial distribution with n = 15 as p changes from. 50 toward. 05 the distribution will__________?
- 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 distribution develops positive skewness. Therefore, it becomes more positively skewed.
Correct answer: Become more positively skewed64. In a binomial distribution, n = 10 p= 3/5, its mean is:_________________?
- 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.
Correct answer: 665. Which of the following case is true for hyper geometric distribution________________?
- 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 trials are dependent. Hence both (b) and (c) are true.
Correct answer: Both (b) & (c) but not (a)66. The binomial distribution is symmetrical when:______________?
- 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. Statements (b) and (c) express the same condition, making (d) correct.
Correct answer: Both (b) & (c) but not (a)67. What is the mean of binomial distribution ____________?
- 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. The other expressions are either the variable or a general mean formula, not the specific binomial result.
Correct answer: n x p68. Binomial probability distribution is denoted by b(x ; n, p), is defined as _______________?
- 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. Option (a) represents this formula; the other expressions have incorrect or incomplete powers.
Correct answer: {nx}px qn-x69. There are ____________ parameter in Binomial distribution?
- 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. q is not an additional parameter because q = 1 − p.
Correct answer: n, p70. The experiment is repeated a _____________ number of times?
- 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. “Trial” names each repetition, not the number of repetitions.
Correct answer: Fixed