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Unformatted text preview: X 2 ) E ( Y 2 ) (1) (Hint: Use the fact that for any real a , E (( X + aY ) 2 ) ≥ 0.) 5. Two continuous random variables X and Y are described by the pdf f XY ( x,y ) = c, if  x  +  y ≤ 1 √ 2 , otherwise (2) where c is a constant. a) Find c . b) Find f X ( x ) and f X  Y ( x  y ) . c) Are X and Y independent random variables? Justify your answer. Problem d is an optional question, those who solve it will get extra credits. d) De±ne the random variable Z = (  X  +  Y  ). Find the pdf f Z ( z ). 2...
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 Fall '04
 Chow
 Probability theory, geometric random variable, Gaussian random vector

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