A certain random variable \(X\) has moment-generating function
\[ M(t)=\frac{e^{2t}}{1-3t},\quad t<1/3. \]
- Compute the mean and variance of \(X\).
- What is the moment generating function of the new random variable
\[ Y=\frac{\pi}{2}-\frac{X}{3}. \]
A certain random variable \(X\) has moment-generating function
\[ M(t)=\frac{e^{2t}}{1-3t},\quad t<1/3. \]
\[ Y=\frac{\pi}{2}-\frac{X}{3}. \]