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 11 of 14
101. The hypergeometric probability distribution is used rather than the binomial or Poisson when the sampling is performed ?
- 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 changes after each draw. With replacement, trials remain independent and binomial modelling is appropriate.
Correct answer: With out replacement from a finite population102. When X denotes the number of success in binomial experiment, it is called ________________?
- 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. It is also a random variable in the general sense, but it is discrete rather than continuous.
Correct answer: Binomial random variable103. In binomial experiment successive trials are ______________?
- 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. This condition, together with a constant success probability and two outcomes, defines the binomial experiment.
Correct answer: Independent104. In binomial experiment, the successive trials are _____________?
- 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. “Constant” describes the probability of success, not the relationship between trials.
Correct answer: independent105. In the binomial experiment, the outcomes of each trial maybe classified into ______________?
- 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. The labels do not imply that success is favourable or failure is undesirable.
Correct answer: Success or Failure106. A binomial random variable can assume values from _________ to n?
- 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 trial. Therefore the lower limit is 0.
Correct answer: 0107. In binomial distribution the probability of success remains __________ from trial to trial?
- 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. If that probability varies, the standard binomial model no longer applies.
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 distribution. The t distribution has heavier tails for finite degrees of freedom, not lighter tails as option c suggests.
Correct answer: Greater the degree of freedom, the more the t-distribution resembles the standard normal distribution109. The t distribution are_____________?
- 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 freedom. It is therefore not skewed.
Correct answer: Symmetrical110. Which of the following is an assumption underlying the use of the t-distribution ?
- 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. The population variance is unknown, while s², not s itself, is an unbiased estimator of the population variance.
Correct answer: The sample are drawn from a normally distributed population.