***please only answer question3

Exercise 4.1 (Aww - Likelihood principle and p-values (50%)). (Background) Suppose that, in a social media "FaceLook", advertisements may pop up to selected users accordingly to a deep-learning (DL) algorithm. If a selected user clicks into the advertisement, then we say that the algorithm successfully selects a correct user. Let & 15%. (4.1) Denote success and failures by 1 and 0, respectively. FaceLook obtains the following dataset 010 0 0 001 10 10 010 1. (Experiment 1) Suppose that the algorithm selects 15 users. It records 5 successes. Then it is reasonable to model the number of successes by X - Bin(15, #), whose PMF is fo = (15)07(1 -0)15-=1(x = 0, . .., 15). (a) (10%) Derive the likelihood function L(0 | X). (b) (10%) Explain why the p-value for testing (4.1) is p = Eres fo.Is(I). Is Ho rejected at 5% level? 2. (Experiment 2) Suppose that the algorithm repeatedly selects users until 10 failures. It takes 15 trials. Then it is reasonable to model the number of trials needed by N - 10 + NB(10, 0), whose PMF is fe(n) = (10_1)92-10(1 -0)101(n = 10, 11, ...). (a) (10%) Derive the likelihood function L(0 | N). (b) (10%) Explain why the p-value for testing (4.1) is P = En-is fo.15(n). Is Ho rejected at 5% level? 3. (10%) Do p-values obey the likelihood principle? Explain. What does it mean in practice?3. Is L(0 | X)