NEED URGENTLY WITHIN 10 HOURS. ONLY ONE STATISTIC QUESTION

Quesn: Your friend flips a fair coin n times and tells you how many heads showed up. She does not tell you how many times she flipped the coin. She repeats this experiment 10 times (each experiment has n flips), and reports to you the number of heads for each experiment: x1, x2, . . . , x10.

(a) Give an unbiased statistic, , that you would use to estimate n. Please include an argument for why the bias is zero.

(b) R Code: Simulate this experiment 1,000 times with n = 25 (each simulation will produce a list of 10 numbers). Use your statistic is part (a) to estimate n for each simulation (you should end up with 1,000 values for ).

(c) R Code: Plot a boxplot of your 1,000  values. Draw a horizontl red line where the true value of n is. Are your values centered roughly around the true value of n?

(d) R Code: Plot of histogram of your 1,000  values. What type of continuous distribution do you think would fit these well?

(e) R Code: Estimate the parameters of the distribution of your values (the distribution you answered in part (d)). Plot the pdf of this distribution on top of your histogram from part (d).