Question

RI. Suppose X is a continuous RV with E(X)-μ and Var(X)-σ2 where both μ and σ are unknown. Note that X may not be a normal distribution. Show that X is an asymptotically unbiased estimator for μ. (This problem does not require the computer.) R2. Let X ~ ŅĢi-10.82). Following up on RI, we will be approximating μ2, which we can see should be 100. For now, let the sample size be n = 3, Pick 3 random numbers from X, compute ー2 X, and repeat the process a total of 50000 times. Plot a smooth version of the histogram of these 50000 values for X: the plot (density (..) command in R wl be useful. Now find the average of your 50000 values and make a vertical dotted line in R at this number (match the color of your curve). You have just made a rough picture of the density function for X (when n 3) and identified its (approximate) expected value. Now you should repeat this process for n = 6, n 10 and n = 50, Plot all four of these curves (use different colors) and vertical lines on the same set of axes choosing limits on the axes so the picture looks nice. Finally, put a dark solid vertical line at100. You should be able to see the asymptotic unbiasedness in the picture. Your answer is your code and a rough sketch of the plot you have created

Answer 1