Consider the random varia

Consider the random varia

Consider the random variable, whereis an unknown parameter andis a random variable with expected value zero.a. What is the expected value of Y?b. Suppose you have a random sampledrawn from the distribution for Y.Derive the least squares estimator for. A least squares estimator is an estimator M which minimizes the sum of squared residuals:c. Is M a random variable? Why?d. Suppose that Y is independently normally distributed with variance 1.What are the mean and variance of M?What form does the distribution of M have?e. Suppose you want to test the null hypothesisagainst the alternative that. If the sample size is 49 and you use a 0.05 significance level, what values of Y would lead you to reject the null hypothesis under the assumptions in (d)?

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