statsps3 - pdf of X (b) Find Pr( X < 1 = 4) (c)...

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Problem Set 3 Probability and Statistics Bernardo Guimaraes September 2009 1. Consider 2 independent and normally distributed random variables ( X;Y ), with the same distri- bution: X = Y = = 2 and ± 2 X = ± 2 Y = ± 2 = 4 . U = ( X + Y ) = 2 , V = ( X + Y ) , W = 2 :X . You can use p 2 = 1 : 4 . Find: (a) Pr( X > 3) , (b) Pr(1 < X < 3) , (c) Pr( U > 3) , (d) Pr(1 < U < 3) , (e) Pr( V > 6) ; (f) Pr(2 < V < 6) ; (g) Pr( W > 6) , (h) Pr(2 < W < 6) : 2. The pdf of X is f X ( x ) = 2 x , for 0 < x < 1 (and 0 otherwise). (a) Graph the
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Unformatted text preview: pdf of X (b) Find Pr( X &lt; 1 = 4) (c) Find and graph the pdf of Y = X 2 (d) Find Pr( Y &lt; 1 = 16) (e) Find and graph the pdf of Z = p X (f) Find Pr( Z &lt; 1 = 2) (g) Find and graph the pdf of W = e X (h) Find Pr( W &lt; e 1 = 4 ) (i) Find and graph the pdf of U = log( X ) (j) Find Pr( U &lt; log(1 = 4)) 1...
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