5. The number of tornadoes per year to hit a particular town follows a Poisson distribution with mean \(\lambda\). A weatherman claims that due to climate changes the mean number of tornadoes per year has decreased. He records the number of tornadoes \(x\) to hit the town last year. To test the hypotheses \(\mathrm { H } _ { 0 } : \lambda = 7\) and \(\mathrm { H } _ { 1 } : \lambda < 7\), a critical region of \(x \leq 3\) is used.

1. Find, in terms \(\lambda\) the power function of this test.
2. Find the size of this test.
3. Find the probability of a Type II error when \(\lambda = 4\).