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Q1_Math308_608 - Quiz 1 Math 308/603 January 22 1 Let...

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Unformatted text preview: Quiz 1 Math 308/603, January 22 1. Let X1,X2,...,X,. be independent random variables with E(Xg) = p. and Var-(X 1‘) = 0”. Find the mean and \a‘axciance of the sample mean 3; = 32;: E: n n ' 2. Suppose W,X,Y are independent normal random variables with means 3, 4, and 5 respectively. Suppose each has standard deviation 7. Use these to construct ‘ a. a chi-squared random variable lwith 3 degrees of freedom, x§ b. a. t random variable with 2 degrees of freedom, t2. 3. Show that if X ~ mea then X‘1 ~ me. QMii ’f Re); Mffik 308/608/ aqnum/y 32' n ('1 in: Xfly‘zé EEQXsz—éél =J.A EKX>=E n "(-1 ‘ — V ‘— = .L h‘ ..I r‘ ,_ (MUM Vaa n 5 X‘ "6‘ VGA [2. XQ - "I 1‘ L 1 ‘L V 1' l“- 7'2. é- 7‘ “I E! “4X0 h“ 5'6 “ .5;th :h ALAflnéfith \A/N N(‘312)/ X61 y(4/}1)/ YuA/(g/J'L) (ax/L .r‘XSEQ/IM,‘ “mm X Awe; _ ~4 [-5 . Curt 0J5“ “\th AMA‘ ILMJ‘ a :L z 1‘ «37. x~qi YflgL it ) {I‘ll-22+2}- 3 )+(-:_; )+k E N .5 19 iii-5 2 ET - L 4- V5?— M it. (2540/2 Egpkg )3/‘2. fie-l X“) ‘n/m 1Q. 5%; bf [AN n)v»/r’ h I-'\A ‘ QJ‘] il_ M/fl “id VIM N X '(w/m) ‘ am PM ...
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