Question

If the slope of the CDF at a point is 0; Select one: a. The PDF of the random variable at the point is also 0. b. The PDF of the random variable cannot be determined with this information. c. The PDF of the random variable at the point is infinity. d. The PDF of the random variable at the point is 1.

Answer 1

We know that the relationship between CDF and PDF is that PDF is the derivative of CDF.

So PDF at a point is the derivative of CDF at the same point.

Slope means the derivative of one variable over other.

The derivative measures the steepness of the graph of a function at some particular point on the graph. Thus, the derivative is a slope. That means that it is a ratio of change in the value of the function to change in the independent variable. So slope ofof CDF at a point is zero means derivative of that variable at the point is zero implies the PDF is zero.

So option one, PDF of that random variable at that point is zeo