1. Given five data values x=[1, 4, 6, 9, 15). Show the hand calculations of the mean (xavg) and standard deviation (xstd), using the formulas xavg = (1/N) * (x) xstd = [1/(N-1) * [ (x - xavg) ? ] Verify using MATLAB's mean and std functions. mean(x) std(x) 2. Create the MATLAB function prob shown below, which calculates the probability (in percent) of r out of n occurrences of independent events, each occurring with probability of /2 (50%). >>f=@(n) factorial(n); >> prob=@(r,n) f(n)/(f(r)*f(n-r))/(2^n)*100; The answer is obtained by entering P=prob(r,n) with r and n replaced by integer values. ind the probabilities below. Show your MATLAB statements and the answers. (a) Find P1, the probability in percent of getting exactly 10 heads out of 20 coin tosses. P1 = (b) Find P2, the probability in percent of getting between 8 and 12 heads out of 20 coin tosses. Hint: Add the probabilities of 8 to 12 out of 20 since they are mutually exclusive events. Note that prob(9,20) = prob(11,20) prob(8,20) = prob(12,20) P2 = (c) Find P3, the probability in percent of getting at least 17 heads out of 20 coin tosses. >> P3 =