Question

Which of the following statements are correct?
(A) In case of a continuous random variable X, the cumulative distribution function can be obtained by carrying out a derivation of the probability distribution function with respect to x.
(B) In case of a discrete random variable X, the cumulative distribution function can be obtained by carrying out a derivation of the probability distribution function with respect to x.
(C) In case of a continuous random variable X, the probability distribution function can be obtained by carrying out a derivation of the cumulative distribution function with respect to x.
(D) In case of a discrete random variable X, the probability distribution function can be obtained by carrying out a derivation of the cumulative distribution function with respect to x.

• (A) and (B) only
• (A) only
• (C) only
• (C) and (D) only

Hint:

For continuous random variables, the PDF is the derivative of the CDF, and for discrete random variables, it's the difference.

Answer 1

The Correct Option is C

(A) For a continuous random variable, the cumulative distribution function (CDF) is the integral (not derivative) of the probability distribution function (PDF) with respect to x.
(B) For a discrete random variable, the CDF is calculated by summing the probabilities up to x.
(C) The PDF is the derivative of the CDF for continuous random variables.
(D) The PDF for a discrete random variable can be obtained by the difference of CDF values.
Thus, the correct answer is (c).