The sum of the values obtained in a random sample of size n = 5 is to be used to test the null hypothesis that on the average there are more than two accidents per week at a certain intersection (that λ > 2 for this Poisson population) against the alternative hypothesis that on the average the number of accidents is two or less. If the null hypothesis is to be rejected if and only if the sum of the observations is five or less, find

(a) the probabilities of type I errors when λ = 2.2, 2.4, 2.6, 2.8, and 3.0;

(b) the probabilities of type II errors when λ = 2.0, 1.5, 1.0, and 0.5.

Also, plot the graph of the power function of this test criterion.