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 13 of 14
121. For a probability density function (pdf), the probability of a single point is_____________?
- A. 1
- B. 2
- C. 0
- D. Constant
Explanation: For a continuous random variable, probability is assigned to intervals, not individual points, so P(X = x) = 0. A single point has zero width under the probability density curve.
Correct answer: 0122. The distribution function F(X) is represent by_______________?
- A. P(X=x)
- B. P(X
- C. P(X>x)
- D. P(X≤x)
Explanation: The distribution function is the cumulative probability up to and including x, written F(x)=P(X≤x). P(X=x) gives only the probability at one value and is not the distribution function.
Correct answer: P(X≤x)123. The probability function is always______________?
- A. Negative
- B. Non Negative
- C. Positive
- D. None
Explanation: A probability function cannot assign a negative value, so it is non-negative for every possible outcome. It may equal zero, which is why “positive” is less accurate than “non-negative.”
Correct answer: Non Negative124. A discrete probability distribution may be represented by____________?
- A. A Table
- B. A Graph
- C. A mathematical Equation
- D. All of these
Explanation: A discrete probability distribution can be listed in a table, displayed graphically, or expressed through a mathematical formula. Hence all three forms are valid.
Correct answer: All of these125. For discrete random 'X', the expectation of X i.e., E(x) is equal to:________________?
- A. ∑P(x)
- B. ∑x.P(x)
- C. ∑x2P(x)
- D. One
Explanation: For a discrete random variable, expected value is obtained by multiplying each value by its probability and summing: E(X)=∑xP(x). The other sums represent total probability or, in the squared case, a second-moment quantity.
Correct answer: ∑x.P(x)126. If a & b are constants, then Var (a + bX) equal to_________________?
- A. Var(bX) + a
- B. b2 Var(X)
- C. b Var(x)
- D. None of these
Explanation: Adding a constant does not change variance, while multiplying a variable by b multiplies its variance by b². Thus Var(a+bX)=b²Var(X).
Correct answer: b2 Var(X)127. A random variable is ____________ ?
- A. Not a function
- B. A continuous variable
- C. A function
- D. None of these
Explanation: A random variable is a function that assigns a real number to each outcome in the sample space. It may be discrete or continuous, so it is not necessarily a continuous variable.
Correct answer: A function128. A function probability that a random variable of x has a value less than is called _____________?
- A. Random function
- B. Distribution function
- C. Continuous function
- D. probability function
Explanation: The distribution function, or cumulative distribution function, gives the probability that X is less than or equal to a specified value: F(x) = P(X ≤ x). A probability function usually refers instead to a probability mass or density function.
Correct answer: Distribution function129. A random variable may be _____________?
- A. fixed
- B. continuous
- C. discrete
- D. discrete or continuous
Explanation: A random variable can have countable outcomes, making it discrete, or values over an interval, making it continuous. Therefore, both types are possible.
Correct answer: discrete or continuous130. If E(x) is the expected value of X then E[x - E(x)]= ___________________?
- A. E(x) - E(x)
- B. E(X) - 0
- C. 0
- D. E(x) + E(x)
Explanation: Using the linearity of expectation, E[X − E(X)] = E(X) − E(X) = 0. Subtracting a random variable's own mean produces a deviation whose average is zero.
Correct answer: 0