hw1 - Stat 704, Fall 2011: Homework 1 Due Sept. 1 1. Let Y...

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Unformatted text preview: Stat 704, Fall 2011: Homework 1 Due Sept. 1 1. Let Y 11 ,Y 12 ,...,Y 1 n 1 iid N ( 1 , 2 1 ) , independent of Y 21 ,Y 22 ,...,Y 2 n 2 iid N ( 2 , 2 2 ) . Let Y 1 = 1 n 1 n 1 i =1 Y 1 i and Y 2 = 1 n 2 n 2 i =1 Y 2 i be the sample means from the two popula- tions. (a) Find E ( Y 1- Y 2 ). (b) Find var( Y 1- Y 2 ). (c) What is the distribution of Y 1- Y 2 ? Hint: first find the distributions of Y 1 and Y 2 and argue that these two random variables are independent. 2. Let Y 1 , Y 2 , and Y 3 be independent random variables with means E ( Y i ) = i for i = 1 , 2 , 3 and common variance var( Y i ) = 2 . Define Y = 1 3 ( Y 1 + Y 2 + Y 3 ). (a) Find cov( Y 1- Y , Y ). (b) Find E { ( Y 1 + 2 Y 2- Y 3 ) 2 } . 3. A random sample of 796 teenagers revealed that in this sample, the mean number of hours per week of TV watching was y = 13 . 2, with a standard deviation of s = 1 . 6....
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This note was uploaded on 12/14/2011 for the course STAT 704 taught by Professor Staff during the Fall '11 term at South Carolina.

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hw1 - Stat 704, Fall 2011: Homework 1 Due Sept. 1 1. Let Y...

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