Help me plss Stats

1. Write a Jupyter notebook for the following simulation exercise. Consider the linear model Yi = a + Bx; + e; where x; ~ f.(02), e; ~ fe(0e) and fx fe are PDFs of some random variable. I; and e; are independent. For this question, assume that fx and fe are both standard normal distribution but we will consider different distributions below. Assume that a = B = 1. (a) What are the theoretical properties of the OLS estimators and B? What is their theoretical distribution given a sample size N? (b) Draw Mi.i.d. random samples of length N for ; and e;. Start with M = 5000 and N = 50 but you should experiment with different values. For each m= 1, ..., M, compute the OLS estimators m and Bm and their standard errors. Compute the means and standard deviations of the distribution of the M estimators m and Bm (e) Plot the histograms of the Mm and Bm. (d) Compare the distribution of the simulated m and Bm to their theoretical distribu- tions. 2. Repeat the exercise in question 1 but assume that x; and e; are correlated with a correlation coefficient of Pue = 0.5. 3. Repeat the exercise in question 1 but assume that fx fe are both t-distributions with 5 degrees of freedom. 4. Repeat the exercise in question 1 but assume that fx fe are both uniform distributions U[0,1]. 5. Experiment with different sample sizes, e.g. set N to 100, 500, ... You do not have to report all results in detail but describe the effect of N on the behavior of the OLS estimators in the questions above