All Free Statistics MCQs with Answers

• 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. 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).

• 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.

• 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.

• 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).

• 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).

• 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.

• 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…

• 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.

• 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…

• A. Discrete
• B. Variable
• C. Scale
• D. Non of these

Explanation: A discrete random variable is defined on a discrete sample space, whose outcomes can be listed or counted.

• A. a discrete variable
• B. a continuous variable
• C. a constant
• D. a qualitative variable

Explanation: The sum of two dice can take only the integer values 2 through 12, giving a finite set of possible outcomes.

• A. P(AorB) =0
• B. P(AandB)=0
• C. P(AnorB)=0
• D. P(AeitherB)=0

Explanation: Mutually exclusive events cannot occur together, so their intersection is empty and P(A and B) equals zero.

• A. Dependent
• B. Independent
• C. Overlapped
• D. None of These

Explanation: Mutually exclusive events cannot occur together, whereas independent events can occur together without affecting each other, so mutually…

• A. It must have a value between 0 and 1
• B. It can be reported as a decimal or a fraction
• C. A value near 0 means that the event is not likely to occur/happens
• D. It is the collection of several experiment

Explanation: A probability is a numerical measure between 0 and 1 and may be written as a decimal or fraction; a value near 0 indicates an unlikely…

• A. Independent
• B. Mutually exclusive
• C. Bayesian
• D. Empirical

Explanation: The special multiplication rule, P(A∩B) = P(A)P(B), applies when events are independent.

• A. 4/36
• B. 13/36
• C. 21/36
• D. 15/36

Explanation: There are 11 outcomes with at least one 4 and 6 outcomes whose sum is 7; 2 outcomes belong to both groups.

• A. Independent
• B. Mutually Exclusive
• C. Bayesian
• D. Empirical

Explanation: If occurrence of one event rules out the occurrence of another, their intersection is empty, so they are mutually exclusive.

• A. 5
• B. 5×5
• C. 1
• D. None of these

Explanation: Choosing all 5 objects from 5 gives only one possible selection, so \(\binom{5}{5}=5!/(5!0!)=1\).

• A. 1.2.3.4,.........
• B. 1.2.3......(n-2) (n-1) (n)
• C. n. (n-1) (n-2)..............3.2.1.0
• D. None of these

Explanation: The product of the first n natural numbers is 1 × 2 × 3 × ⋯ × n, which is written as n!. Option b expresses this product in ascending order.