MATLAB PROBLEM: When you take data from some complex engineering situation, you often do not know what distribution the data follows. Lets mimic that situation here by studying the process that generates N random numbers x as x=rand(N,1).^0.2, i.e., a uniform random variable raised to the 1/5th power. SHOW CODE PLEASE TO HELP ME CORRECT MY WORK.

(a) Start by getting a feel for what the distribution looks like by drawing histograms for dierent values of N using dierent widths of the histogram bars. Can you guess what the probability density function f(x) is?

(b) Use N = 1000 to compute a 95% condence interval on the mean . Hint: use the Central Limit Theorem.

(c) For N = 1000 samples, can you estimate a 95% condence interval on the variance 2? This is not something we have done in class, so you need to think a bit here. Hint: Remember that the whole denition of a 95% condence interval is that it will contain the true value 95% of the time. So if you sample N = 1000 once and nd the sample variance s2, and then repeat this same calculation (i.e., in a loop) a total of m times (where m is rather large), then the condence interval is the interval that contains the middle 95% of those s2 values. Another hint: draw a histogram of the s2 values you found.