1. Let /(x) = 1/r, 1 x oo, zero elsewhere, be the p.d.f. of a random variable X. Consider a random sample of size 72 from the distribution having this p.d.f. Compute approximately the probability that more than 50 of the observations of the random sample are less than 3.
2. Forty-eight measurements are recorded to several decimal places. Each of these 48 numbers is rounded off to the nearest integer. The sum of the original 48 numbers is approximated by the sum of these integers. If we assume that the errors made by rounding off are i.i.d. and have uniform distributions over the interval (-!,!), compute approximately the probability that the sum of the integers is within 2 units of the true sum.