Prob18W-04.pdf - ELG 3126 RANDOM SIGNALS AND SYSTEMS Winter...

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ELG 3126 RANDOM SIGNALS AND SYSTEMS Winter 2018 ASSIGNMENT 4 (due at 11:30 AM Thursday, Feb. 8 in class) 1. From the text: 3.9. Assume that each coin toss is an independent experiment with the same probability of “Heads.” 2. From the text: 3.19, but make p = 0 . 075. 3. An information source produces a pair of binary symbols with four possible values. A random variable X is defined by mapping one binary pair value to 1, another to 2, a third to 3, and the last to 4. Let p k , P ( X = k ) for k = 1 , 2 , 3 , 4. (a) Sketch the cdf of X , F X ( x ), for each of the three cases (i) p k = p 1 / ( k + 1) for k = 2 , 3 , 4, (ii) p k +1 = p k / 3 for k = 1 , 2 , 3, (iii) p k +1 = p k / 2 k for k = 1 , 2 , 3. (b) Use the cdf to find the probabilities P ( X ≤ - 1), P ( X < 1 . 5), P (0 . 5 < X 2 . 999), P (1 < X 4). 4. A dart is equally likely to land at any point inside a circular target of radius 3 units. A random variable R is define to be the distance the point where the dart lands is away from the target centre. (a) What is the sample space for this experiment and what is the mapping from the sample space to R that R
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