arts (a), (b), and (c) need to be done on R programming language. Let X be a continuous random variable with the following probability density function f(x) = {(3x2/2), for x∈[−1,1]            {0 otherwise   (a) The population mean is 0. Simulate a dataset of n = 500 random draws from the distribution. Construct the 95% confidence interval of the population mean from the dataset. (b) Repeat part (a) m = 100 times. Compute the percentage of times (denoted by p) the constructed confidence interval contains E(X) (c) Repeat part (b) with m = 200; 500; 1000; 2000; 5000; 10000; 20000;  Produce a plot of the percentage p vs. the number of intervals m.

Parts (a), (b), and (c) need to be done on R programming language.

Let X be a continuous random variable with the following probability density

function

f(x) = {(3x²/2), for x∈[−1,1] 

          {0 otherwise
 

(a) The population mean is 0. Simulate a dataset of n = 500 random draws from the distribution. Construct the 95% confidence interval of the population mean from the dataset.

(b) Repeat part (a) m = 100 times. Compute the percentage of times (denoted by p) the constructed confidence interval contains E(X)

(c) Repeat part (b) with
m = 200; 500; 1000; 2000; 5000; 10000; 20000; 

Produce a plot of the percentage p vs. the number of intervals m.