\(X\) possesses the goofy distribution if its PDF is:

\[ f(x)=k\frac{x^{k-1}}{\theta}\exp\left(-\frac{x^k}{\theta}\right),\quad x>0. \]

The constants \(k\) and \(\theta\) are both positive parameters. We denote this \(X\sim\text{GF}(k,\,\theta)\)

1. If we define a new random variable \(Y=\ln X\), what is its distribution?
2. If we define a new random variable \(Z = X^k\), what is its distribution?