Assignment #1, STAT331/361/SYDE334 Winter 2007 This assignment is to be handed in at the start of the lecture of Thursday 18th January, 07 . For some problems required the application of R software, you need to cut and paste results (either numeric or graphic) into Word, which can then edited, commented on and handed in. DO NOT hand in R code, or a print out of the R session, unless asked for. Problem 1 : Let y be the sample mean of observations y 1 ,...,y n . (a) Show that n X i =1 ( y i-y ) 2 = n X i =1 y i ( y i-y ) . (b) Rewrite the above result in a matrix notation. For example, one may write ∑ n i =1 a i = 10 a , where 1 = (1 ,..., 1)0 is an n-dimensional vector of all ones and a = ( a 1 ,...,a n )0 is the other n-dimensional vector. Problem 2 : Consider a normal random variable X ∼ N (2 , 4) or X ∼ G (2 , 2). (a) Find mean E( X ), variance var( X ), and the second moment E( X 2 ). (b) Show that
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