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 $P(X> 2c)$.
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