Please fill the blanks for the following questions with explaination.

Part I. [16 points] Fill in the blanks for the following questions 1. If X is an unbiased estimator of a and Y is an unbiased estimator of B, then is an unbiased estimator of a +B. 2. If X is an unbiased estimator of a and Y is an unbiased estimator of B, then X*Y is an estimator of aB. 3. An analyst plans to use the following test statistic: X - Ho tru = s/ Vn This statistic is appropriate for a hypothesis about the of a normal distribution with unknown variance. 4. If X1, X2, ..., XN are independent standard normal random variables, then the distribution of the random variable X, where X = X12 + X22 + ... +XN, is a distribution. 5. A test statistic must be under the null hypothesis. 6. If a return Y follows a normal distribution N(0, o2), then an efficient and unbiased estimate of o' for a random sample y1, y2, ..., yn is 7. Given a random normal sample x1,x2, ...Xn drawn from N(u, ?), the sample mean x = - Ex, will follow a normal distribution n 1=1 with E( E(x) = M and Var(x) = 8. The level of significance is the of running a Type I error