solutionsMAUEXAM2

# solutionsMAUEXAM2 - Problem I(a Given XI and X2 are...

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Problem I: (a) Given XI and X2 are independent normal random variables: - N (20,22], Xz -N (15, lL), Find: 6) E(Y)= ~E(~I)-~ECX~L)+~ = 3(20)-2(15)+5 = 35 ii v (u) = 327/&1) t z2v(x4 \$-o q(d)+~ (I) = 40 (iii) Probability distribution of Y - N ,+c e (b) Suppose U V are norma1 random variables: V - N (20, 32), Cov (U, V) = 3 L (i) Find the correlation coefticient p,, = bucu,~)- - 3 - ---- ;= Ld.25 5 * rv (4x3) 4

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Fill in the blanks in the following: (a) If sample from a population N((20, 22), yield oi = 0.2, then the sample size bj = - 2 - % = 1 *= fiQ0 JM -r7 (b) TT and ji (median) are taken as point estimators of population mean p then either E or 2 or both (which) are unbiased b 0% (c) Approximately 9 9 . 74 % of the area under a Gaussian is included between p f (d) Samples of size n = 36 are drawn from an arbitrary popuIation. Then sample means E will have an approximately td OX n?d distribution because of theCiwJ-d L4 #-Theorem. ~c LT) (e) What MINITAB command would you use to generate pseudo random numbers with a normal distribution & 7% ~d orz? DR~ 4 N on L (f) The number arrivals at a service facility is a Poisson variable.
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## This note was uploaded on 10/20/2008 for the course ENGR engr2600 taught by Professor N/a during the Spring '08 term at Rensselaer Polytechnic Institute.

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solutionsMAUEXAM2 - Problem I(a Given XI and X2 are...

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