Consider a random variable \(X\) with pdf
\[ f(x;\,\theta) =\begin{cases} \frac{x}{\theta}e^{-\frac{x^2}{2\theta}} & x\geq 0\\ 0 & \text{else}, \end{cases} \]
where \(\theta >0\) is a parameter.
- Compute the CDF of \(X\).
- Compute the median of \(X\).
Consider a random variable \(X\) with pdf
\[ f(x;\,\theta) =\begin{cases} \frac{x}{\theta}e^{-\frac{x^2}{2\theta}} & x\geq 0\\ 0 & \text{else}, \end{cases} \]
where \(\theta >0\) is a parameter.