17. a. You have numbers 2121, . . . , xiv. The mean is E = % 2:le can, and the variance is 2 1 N 2 03 N 211:1(3271 _ a?) ' i. Show that 0': = % 2:le xi 552. ii. Show that for any set of numbers, the average of the squares is as large as the square of the average. iii. How can you compute the variance with just one pass through the data m1, . . . , :rN. b. You have a stream of independent uniform random variables taking on values in [031]- i. How will you generate a uniform random variable in the interval [a, 6]? ii. How will you generate a Gaussian random variable with mean 0 and variance 1? iii. How will you generate a Gaussian random vector x with mean vector p and covariance matrix I]