(Solved): A continuous random variable \( X \) has the density function below. Find the expected value of \( ...

A continuous random variable \( X \) has the density function below. Find the expected value of \( g(X)=e^{\frac{2 X}{5}} \) \[ f(x)=\left\{\begin{array}{ll} 6 e^{-6 x}, & x>0 \\ 0, & \text { elsewhere } \end{array}\right. \] The expected value of \( g(X)=e^{\frac{2 X}{5}} \) is (Simplify your answer.)