Problem 13. Let X1. X; be independent. identically distributed coin flips (taking values I] = failure or 1 = success) having success probability it. Give and interpret the likelihood ratio comparing the hypothesis that n- = .5 (the coin is fair) versus it = 1 [the coin always gives successes) when both coin flips result in successes. Outcome! Ptxlnz HXInall n-Iunsjl 5 0.5 1 2 55 0.25 1 4- 555 0.115 1 l 5555 05525 1 15 55555 0.03125 1 32 The likelihood ratio gives the information that if the coin flips result in successes in a run. it is more likely that 1r :1