A single observation is to be used to test the null hypothesis that the mean waiting time between tremors recorded at a seismological station (the mean of an exponential population) is θ = 10 hours against the alternative that θ ≠ 10 hours. If the null hypothesis is to be rejected if and only if the observed value is less than 8 or greater than 12, find 

(a) The probability of a type I error; 

(b) The probabilities of type II errors when θ = 2, 4, 6, 8, 12, 16, and 20.

Also plot the power function of this test criterion.