Suppose X is a negative binomial random variable with parameters r unknown and p = 0.5. a) find the most powerful test b) compute the power of this test for the alternative r=2 (see the attached picture for complete question)

Problem B . 4 . Suppose * is a negative binomial random variable with parameters unknown and p = 0.5 ( a ) Derive the most powerful test of size a = 0. 125 of Ho : ? = 1 VS Ha T based on the observed value of X ( b ) Compute the power of this test for the alternative r = 2