One generates a number r from a uniform distribution on the

One generates a number r from a uniform distribution on the interval [0, theta]. One decides to test H_0: theta = 2 against H_1: theta notequalto 2 by rejecting H_0 if x lessthanorequalto 0.1 or x greaterthanorequalto 1.9. (a) Compute the probability of committing a type 1 error. (b) Compute the probability of committing a type 2 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<x<1.9|=2.5)=(1.9-0.1)/2.5=1.8/2.5=0.72

So the type error II=0.72

DO THUMBS UP ^_^