1. Give brief answers to each of the following questions, providing a justication for each part. (a) For a set of n observations, $1,...,1:n, with mean i, show that: I}. 2(a- s) = 0. i=1 (b) If A and B are two events such that: P[AU B) = FLA) + P(B) what can be ooncluded about A and B? (c) If the random variable X ~ Bin(7, 0.4), calculate P(X > D]. (d) For a random variable X, can E(X2) be less than (E(X))2? (e) State the sampling distribution of the sample mean, X, when taking a random sample of size n from a N (0, 02} population. (f) When testing H0 :,u = 4 vs. H1 : P '> 4, explain Why an observed sample mean of i: = 3 would not result in the rejection of Ho. (Answer without conducting a full hypothesis test.) (g) Explain what a pvalue is. (h) In the simple linear regression model, the error term, 5,, is assumed to follow which distribution for all i = 1,...,n? (In your answer be sure to state the mean and variance of Ea.)