# STAT135_1 - Stat 135, Fall 2006 HOMEWORK 1 (due Friday 9/8)...

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Stat 135, Fall 2006 HOMEWORK 1 (due Friday 9/8) 1. Let x 1 , x 2 , . . . , x n be a list of numbers with mean μ and SD σ . Show that σ 2 = 1 n n X i =1 x 2 i - μ 2 2. A class has two sections. Students in Section 1 have an average score of 75 with an SD of 10. Students in Section 2 have an average score of 60 with an SD of 10. a) If possible, say whether the SD of the scores of all the students in the class is (i) less than 10 (ii) equal to 10 (iii) greater than 10 Explain your choice. If it is not possible to make the choice with the information given, explain why not. b) Suppose Section 1 has 30 students and Section 2 has 20. Find the SD of the scores of all the students in the class. 3. The mean as a “least squares” estimate. Suppose we play the following guessing game. You pick a number from the list x 1 , x 2 , . . . , x n , and ask me to guess what it is. My strategy is to guess that the value is some constant c no matter what you pick. Thus for every i in the range 1 through n , the amount of error that I make with my strategy is x i - c . Deﬁne the mean squared error of my strategy to be mse c = 1 n n X i =1 ( x i - c ) 2 Show that the value of c that minimizes mse c is c = μ , and that mse μ = σ 2 . 4. A coin lands heads with probability p . It is tossed 400 times. Compute the boostrap 99% conﬁdence interval for p and compare with the corresponding interval which uses a conservative estimate for the standard error, when the observed number of heads is

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## This note was uploaded on 03/27/2012 for the course MATH 11 taught by Professor Jagoda during the Spring '12 term at Solano Community College.

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STAT135_1 - Stat 135, Fall 2006 HOMEWORK 1 (due Friday 9/8)...

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