An urn contains θ black balls and N − θ white balls. A sample of n balls is to be selected without replacement. Let Y denote the number of black balls in the sample. Show that N n Y is the method-of-moments (MOM) estimator of θ. Note that our sole observation Y is hypergeometric such that E(Y) = Incorrect: Your answer is incorrect. . Thus, the MOM estimator of θ is theta hat = Correct: Your answer is correct. .

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐

let f: r - > r and g: r - > r be two functions defined by f(x) = x + 1 and g(x) = x - 1.

let us prove whether these functions are inverses of each other by using composition.

f·g (x) = f(g(x)) = f(x - 1)

                      = (x - 1) + 1

                      = x

also, g·f (x) = g(f(x))

                  = g(x + 1)

                  = (x + 1) - 1

                  = x

hence, f and g are inverses of each other.

clearly, f·g : r - > r.

therefore, the domain of f·g is r = (-∝, ∝).