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Unformatted text preview: Assignment 6 1. Let X and Y have joint pdf: f X,Y ( x, y ) = k ( x + y ) for ≤ x ≤ 1 , ≤ y ≤ 1 . (a) Find k . (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y . (d) Find P [ X < Y ], P [ Y < X 2 ], P [ X + Y > . 5]. 2. The random vector ( X, Y ) is uniformly distributed (i.e., f ( x, y ) = k ) in the regions shown in the following figures and zero elsewhere. 1 1 ( i ) 1 1 ( ii ) 1 1 ( iii ) (a) Find the value of k in each case. (b) Find the marginal pdf for X and for Y in each case. (c) Find P [ X > , Y > 0]. 3. Let X and Y be independent random variable. Find the expression for the proba bility of the following events in terms of F X ( x ) and F Y ( y ). (a) { a < X ≤ b } ∩ { Y > d } . (b) { a < X ≤ b } ∩ { c ≤ Y < d } . (c) { X  < a } ∩ { c ≤ Y ≤ d } . 1 4. Let X and Y be the jointly Gaussian random variables with the means m 1 and m 2 and variances σ 1 and σ 2 respectively. The pdf is as following: f X,Y ( x, y ) = exp braceleftBigg...
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This note was uploaded on 01/15/2011 for the course ECE 616 taught by Professor Khkjk during the Winter '10 term at Concordia Canada.
 Winter '10
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