One generates a number x from a uniform distribution on the interval [0,theta]. One decides to test H0 : theta = 2 against H1 : theta H1 : theta 2 by rejecting H0 if x 0.1 or x 1.9. Compute the probability of committing a type I error. Compute the probability of committing a type II error if the true value of theta is 2.5. Solution a) P(reject when =2)=P(X<0.1|=2)+P(X>0.9|=2)=(0.1-0)/2+(2-1.9)/2=2*0.1/2=0.1 So the type error I=0.1 b)P(accepting when =2.5)=P(0.1.