Question

In the realm of probability and statistics, when seeking to determine the probability density function (PDF) from a cumulative distribution function (CDF) for a continuous random variable, what is the appropriate method or approach?

a) Differentiate the CDF with respect to the variable
b) Integrate the CDF with respect to the variable
c) Square the CDF
d) Compute the reciprocal of the CDF

Answer 1

The correct approach to determine the probability density function (PDF) from a cumulative distribution function (CDF) for a continuous random variable is to differentiate the CDF with respect to the variable.

Step-by-step explanation:

To determine the probability density function (PDF) from a cumulative distribution function (CDF) for a continuous random variable, the appropriate method is to differentiate the CDF with respect to the variable. In mathematical terms, if F(x) is the CDF of a continuous random variable X, then the corresponding PDF f(x) is given by the derivative of F(x) with respect to x, that is, f(x) = dF(x)/dx. This relationship works because the CDF is the integral of the PDF, and hence, differentiating the CDF yields the PDF.