Gproblem 2i given n i. i.d. random variables x1, x2, . . , xn, each with mean µ and variance σ 2 > 0 (both unknown parameters), we saw in class that the sample mean x = 1 n pn i=1 xi is an unbiased estimator of the mean µ, whereas the so-called sample variance s 2 = 1 n − 1 xn i=1 xi − x ? 2 is an unbiased estimator of the variance σ 2 . in other words, e(s 2 ) = σ 2 . is s = √ s 2 an unbiased estimator of the standard deviation σ? if not, does s tend to underestimate or overestimate the standard deviation? hint: very little computation is needed. start by writing the formula for computing the variance of s

Mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.