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 6 of 7
- A. With replacement
- B. With out replacement from an infinite population
- C. With out replacement from a finite population
- D. With replacement from a finite population
Explanation: The hypergeometric distribution applies when draws are made without replacement from a finite population, so the success probability…
Correct answer: With out replacement from a finite population- A. Random variable
- B. Binomial random variable
- C. Continuous random variable
- D. Both (b) and (c) but not (a)
Explanation: The number of successes in a fixed number of binomial trials is specifically called a binomial random variable.
Correct answer: Binomial random variable- A. Dependent
- B. Independent
- C. May be inependent or dependent
- D. None of these
Explanation: Binomial trials must be independent, meaning the result of one trial does not affect the result of another.
Correct answer: Independent- A. Dependent
- B. independent
- C. Related
- D. constant
Explanation: Successive trials in a binomial experiment are independent, so one trial does not alter the outcome probabilities of the others.
Correct answer: independent- A. Success
- B. Failure
- C. Success or Failure
- D. None of these
Explanation: Each binomial trial has exactly two mutually exclusive outcomes, conventionally labelled success and failure.
Correct answer: Success or Failure- A. 6
- B. 3
- C. 2
- D. 0
Explanation: If X counts successes in n trials, it can take every integer value from 0, meaning no successes, through n, meaning success on every…
Correct answer: 0- A. Constant
- B. Varies
- C. Four
- D. Probability
Explanation: A binomial distribution requires the probability of success, p, to remain constant from one trial to the next.
Correct answer: Constant108. Which of the following is a true statement for comparing the t distribution with standard normal ?
- A. Greater the degree of freedom, the more the t-distribution resembles the standard normal distribution
- B. The Normal Curve is symmetrical whereas the t-distribution are slightly skewed.
- C. The proportion of area beyond a specific value of "t" is less than the proportion of normal curve
- D. Non of these
Explanation: As the degrees of freedom increase, the estimated variance becomes more stable and the t distribution approaches the standard normal…
Correct answer: Greater the degree of freedom, the more the t-distribution resembles the standard normal distribution- A. Symmetrical
- B. None of these
- C. Same as Normal Curve
- D. Skewed
Explanation: The t distribution is symmetric about zero, like the standard normal distribution, although it has heavier tails for finite degrees of…
Correct answer: Symmetrical- A. The sample are drawn from a normally distributed population.
- B. The variance of the population is known
- C. All above
- D. s (sample standard deviation) is an unbiased estimate of the population variance.
Explanation: The usual t procedure assumes that the sample comes from a normally distributed population, especially for small samples.
Correct answer: The sample are drawn from a normally distributed population.- A. The mean and variance of the distribution are same (equal)
- B. The probability of success is always greater than 5
- C. The number of trials is always less than 5
- D. it always contains a contingency table
Explanation: For a Poisson distribution, the single parameter λ determines both its mean and variance, so each equals λ.
Correct answer: The mean and variance of the distribution are same (equal)- A. Random Variable
- B. Contingency table
- C. Bayesian table
- D. Probability distribution
- E. Frequency distribution
Explanation: A probability distribution lists every possible outcome of a random experiment together with its probability, and the probabilities sum to…
Correct answer: Probability distribution- A. 0
- B. -1
- C. 1
- D. Infinity
Explanation: A probability density function must have total area 1 because that area represents the probability of all possible values occurring.
Correct answer: 1- A. A
- B. a E(x)
- C. x E(a)
- D. Non of these
Explanation: A constant factor can be taken outside an expectation, giving E(ax) = aE(x). This is the scaling property of expected value.
Correct answer: a E(x)- A. Trial
- B. event
- C. Experiment
- D. Random experiment
Explanation: A random variable assigns a numerical value to the outcome of a random experiment, such as the number shown when a die is rolled.
Correct answer: Random experiment- A. Random experiment
- B. random Errors
- C. Random digits
- D. None of these
Explanation: Random numbers are commonly generated as random digits, usually from 0 to 9.
Correct answer: Random digits- A. Interval
- B. Point
- C. Time
- D. Sample space
Explanation: A continuous random variable can take any value within an interval, including fractional values.
Correct answer: Interval- A. k Var (Y)
- B. k2 Var(Y)
- C. Var(Y)
- D. k2
Explanation: Multiplying a random variable by k multiplies its variance by the square of k: Var(kY) = k²Var(Y).
Correct answer: k2 Var(Y)- A. Var(X) + Var (Y)
- B. Var(X) - Var (Y)
- C. Var (X)±
- D. Zero
Explanation: For independent variables, the covariance is zero, so Var(X ± Y) = Var(X) + Var(Y).
Correct answer: Var(X) + Var (Y)- A. Zero
- B. C
- C. 1
- D. 2
Explanation: The expected value of a constant is the constant itself, because it has the same value in every possible outcome: E(C) = C.
Correct answer: C