In each case below, identify whether the null and the alternative hypotheses are simple or composite hypotheses.

(a) You are random sampling from a gamma population distribution and you are testing \(H_{0}: \alpha \leq 2\) versus \(H_{a}\) : \(\alpha>2\).

(b) You are random sampling from a geometric population distribution and you are testing \(H_{0}: p=.01\) versus \(H_{a}: p>.01\).

(c) The joint density of the random sample \(\mathbf{Y}=\mathbf{x} \boldsymbol{\beta}+\boldsymbol{\varepsilon}\) is \(N\left(\mathbf{x} \boldsymbol{\beta}, \sigma^{2} \mathbf{I}ight)\) and you are testing whether \(\boldsymbol{\beta}=\mathbf{0}\).

(d) You are random sampling from a poisson population distribution and you are testing \(H_{0}: \lambda=2\) versus \(H_{a}\) : \(\lambda=3\).