1. Given a random sample {y₁, y₂, …, y_n} drawn from N(0, s²). We construct the estimator of s² as follows:

Answer the following questions:

(1) If estimator s² is unbiased, what should be the value of d? Demonstrate your claim mathematically.

(2) Given d in (1), is s an unbiased estimator of ? Explain briefly.

(3) Given d in (1), is s a consistent estimator of ?  Explain briefly.