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 12 of 14
111. In a Poisson probability distribution __________________?
- 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. The other options describe neither a defining property nor a requirement of the Poisson model.
Correct answer: The mean and variance of the distribution are same (equal)112. A listing of the possible outcomes of an experiment and their corresponding probability is called:______________?
- 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 1. A frequency distribution instead reports observed counts or frequencies.
Correct answer: Probability distribution113. Total Area under the curve in probability of density function is ?
- 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: 1114. If E (ax) = _______________?
- 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)115. A random variable is that whose value is determined by the outcome of _________________?
- 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. A mere event is a set of outcomes, not the full process producing the value.
Correct answer: Random experiment116. Random numbers are also called__________________?
- 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. A random experiment is the process used to generate outcomes, not the numbers themselves.
Correct answer: Random digits117. A continuous random variable which can assume all possible values on scale in a given _______________?
- A. Interval
- B. Point
- C. Time
- D. Sample space
Explanation: A continuous random variable can take any value within an interval, including fractional values. This differs from a discrete variable, which takes separate countable values.
Correct answer: Interval118. Var (kY)= ____________?
- 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). Variance measures squared deviations, which is why k is squared.
Correct answer: k2 Var(Y)119. For two independent random variables X & Y, Var (x ± 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). The sign does not change the result because the coefficient of Y is either 1 or -1, and both are squared.
Correct answer: Var(X) + Var (Y)120. If c is non-random variable, the E(C) is_______________?
- 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. It is not zero unless C itself is zero.
Correct answer: C