Hey, I find this problem quite difficult to handle,I would be grateful to anyone who could at least lead on the path of solving it.
The random variable X has a Poisson distribution with mean µ. The value of µ is known to be either 1 or 2 so the following hypotheses are set up.
$H_0$ : µ = 1; $H_1$ : µ = 2
A random sample $x_1$ , $x_2$ , ..., $x_{10}$ of 10 observations is taken from the distribution of X and the following critical region is defined.
\begin{eqnarray*} \sum_{i\in 1}^{10}x_i \geqslant 15 \end{eqnarray*}
Determine the probability of a Type 1 and Type 2 errors.