Let be a positive real number, which is unknown. Suppose the Xi are independent for i

Let θ be a positive real number, which is unknown. Suppose the Xi are independent for i = 1,...,n, with a common distribution Pθ that depends on θ: Pθ {Xi = j } = c(θ )(θ + j )−1(θ + j + 1)−1 for j =

0, 1, 2,.... What is c(θ )? How would you estimate θ? Hints on finding c(θ ). What is ∞

j=0 (aj − aj+1)? What is (θ + j )−1 − (θ + j + 1)−1?