# hw2 - Virginia Tech The Bradley Department of Electrical...

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Virginia Tech The Bradley Department of Electrical and Computer Engineering ECE 5605 – Stochastic Signals and Systems – Fall 08 Problem Set 2 Problem 1. Suppose that a point is selected at random from inside the unit circle. Let Y be the distance of the point from the origin. (a) Find the sample space of Y , S Y . (b) Find the equivalent event in S for the event { Y y } . (c) Find P [ Y y ]. Problem 2. The cdf of the random variable X is given by: F X ( x ) = 1 x > 0 1 / 3 + (2 / 3)( x + 1) 2 - 1 x 0 0 x < - 1 Find the probability of the events A = { X > 1 / 3 } , B = {| X | ≥ 1 } , C = {| X - 1 / 3 | < 1 } , and D = { X < 0 } . Problem 3. The pdf of a mixed random variable is shown in Fig. 1. (a) What is the value of the constant K ? (b) Compute P [ X 5] and P [5 X < 10]. (c) Draw the distribution function. Figure 1: Problem 3. Problem 4. Find f X ( x ) if F X ( x ) = (1 - e - αx ) U ( x - c ), where c 0 and α > 0. Problem 5.

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## This note was uploaded on 05/05/2010 for the course ECECS 5605 taught by Professor Dasilver during the Fall '08 term at Virginia Tech.

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hw2 - Virginia Tech The Bradley Department of Electrical...

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