Unformatted text preview: E[( Y âˆ’ ( A X + B )) 2 ] and E[(( Y âˆ’ Î· Y ) âˆ’ a ( X âˆ’ Î· X )) 2 ] are minimum, then a = A . 5. Let X and Y be two jointly distributed Gaussian random variables having distribution N ( Î· x , Î· y , Ïƒ x , Ïƒ y , r xy ) Let V = a X + b Y and W = c X + d Y . Show that V and W are jointly Gaussian and ï¬nd the parameters that characterize their joint density. 6. Papoulis 72 (82 in 3rd edition). 7. Papoulis 73 (83 in 3rd edition). 8. Papoulis 74 (84 in 3rd edition). ( Hint: Use characteristic Functions) 9. Papoulis 77 (87 in 3rd edition). â€“ 1 â€“...
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 Spring '08
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 Normal Distribution, Standard Deviation, Probability theory, probability density function, Gaussian random variable, Papoulis

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