Chapter 7, Problem 1SYU

To determine

To indicate that the statement “If ${\displaystyle {\int }_{-\infty }^{\infty }p(x)}dx=1$ then $p(x)$ is a density function” is true or false”

Answer to Problem 1SYU

The given statement is “True”

Explanation of Solution

Given information:

The statement“If ${\displaystyle {\int }_{-\infty }^{\infty }p(x)}dx=1$ then $p(x)$ is a density function” is true or false”

True, A density function is a probability function for the continuous random variable and the sum of probability for a random variable is equal to 1. If we try to find the integration for the limit $-\infty$ to $\infty$ for a function and it gives the result equal to 1, then we can conclude that it is a Probability Density function.