Suppose that a random variable $X$ has a probability density function (pdf) given by
\[f(x)=c \exp (-2 x)\]
for $x \geq 1$, and $f(x)=0$, for $x<1$, where $c$ is an appropriate constant so that $f(x)$ is a valid pdf.
What is the expected value of $X$ given that $X \geq 5?$
- $5 \frac{1}{2}$
- $7$
- $10$
- $8 \frac{1}{2}$
- $6$