## Condition that a Function Be a Probability Density Function

## Problem 756

Let $c$ be a positive real number. Suppose that $X$ is a continuous random variable whose probability density function is given by

\begin{align*}

f(x) = \begin{cases}

\frac{1}{x^3} & \text{ if } x \geq c\\

0 & \text{ if } x < c.
\end{cases}
\end{align*}
**(a)** Determine the value of $c$.

**(b)** Find the probability $P(X> 2c)$.