Question

For the distribution function F(x) of a continuous random variable which of the following is not true?
А
F(x) is non-decreasing function of X
В.
F(X) is non-negative function of X
F(x) is step function of X
C
The graph of F(x) is smooth unbroken curve
D
Previous
First​

Answer 1

option C is incorrect ,distribution function is smooth it is not a step function.

Given

• the distribution function F(x)

To find

• incorrect characteristics of the distribution function as mentioned.

Solution

we are provided with the distribution function and many statements related to the distribution function and the asked to find the incorrect statement.

distribution function or probability distribution function is the distribution of all the probabilities of a specific random variable which maybe a discrete or continuous. the distribution functions is commonly represented by F(x) .

The distribution function is always greater than or equal to zero it is also a non decreasing and right continuous function.

since the function is right continuous it would be a smooth curve, distribution function is also a non negative function as the probability of a random variable cannot be negative.

since the graph of the distribution function is smooth it is not a step function.

therefore the option C is incorrect