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 continuous random variables, the cumulative distribution function (CDF) is the integral of the probability distribution function (PDF) with respect to x.
(B) For discrete random variables, the CDF is the sum of probabilities up to a given point x.
(C) For continuous random variables, the PDF is the derivative of the CDF.
(D) For discrete random variables, the PDF is the difference between successive CDF values.
Therefore, option (C) is correct.