Consider two probability density functions on [0, 1]: f0(x) = 1, and f1(x) = 2x. among all tests of the null hypothesis h0 : x ∼ f0(x) versus the alternative x ∼ f1(x), with significance level α = 0.10, how large can the power possibly be?

Aparticular telephone number is used to receive both voice calls and fax messages. suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (a) what is the expected number of calls among the 25 that involve a fax message?