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# HW1 - C b Find P(2 X ≥ Y c Find F X α d Are X and Y...

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1 EE 7615 Problem Set # 1 Due: 9,5,11 1) Please attempt each problem on a new page and write on one side only. 2) Show all your work clearly. 1) Problem 2.16 of the textbook on page 85. 2) Problem 2.17 of the textbook on page 85. 3) Problem 2.18 of the textbook on page 85. 4) The transfer function of a linear system is given by H ( s ) = 1 s 2 + 2 As + 4 . If A is a random variable uniformly distributed over [0 , 10] , ﬁnd the probability that the impulse response of the system is oscilatory. 5) X and Y are two random variables with joint pdf p XY ( x,y ) = ( C x 0 ,y 0 ,x + y < 1 0 otherwise a) Find the constant
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Unformatted text preview: C . b) Find P (2 X ≥ Y ) . c) Find F X ( α ) . d) Are X and Y independent? Justify. 6) X and Y are two random variables with joint pdf p XY ( x,y ) = ( . 25 | x | < y, ≤ y ≤ 2 otherwise Let C be the event that ≤ Y < 1 . a) Find p X ( x | C ) . b) Find E [ X | C ] . 7) X 1 and X 2 are two independent Gaussian random variables each with mean zero and unit variance. Let Y 1 = 2 X 1 + X 2 + 3 (1) Y 2 = X 1-X 2-1 (2) Find the joint probability density function of Y 1 and Y 2 ....
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