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Suppose that a random variable $X$ has a probability density function
\begin{aligned} f(x) & =c(x-4) \quad \text { for } 4 \leq x \leq 6 \\ & =0 \quad \text { for all other } x \end{aligned}
for some constant $c$. What is the expected value of $X$ given that $X \geq 5?$

1. $5 \frac{5}{9}$
2. $5 \frac{1}{2}$
3. $5 \frac{3}{4}$
4. $5 \frac{1}{4}$
5. $5 \frac{5}{8}$