1. Fix r € N, and suppose that Y₁, ..., Yn are independent and identically distributedNegBin(r, ) random variables, each with probability mass function given by¡v (u | 0) – (1 + r − ¹) (1 -fyy(1 - 0) ³0⁰for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negativebinomial is known. (a) By specifying appropriate functions h(y), U(0), T(y) and A(U(0)), show thatthis parametric family is an Exponential Family.(b) Write down a minimal sufficient statistic for 0, justify your answer.dA(c) Using that E{T(Y)}for the parameter==(or otherwise), write down an unbiased estimator

Given that are independent and identically distributed random variables, each with probability…

1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by fy(y | 0) = y (³ + r − ¹) (1 - 0) ³0² Y for y EN and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.