HW4_Spring11_Sol

# HW4_Spring11_Sol - ELEC210 Spring 2011 Homework-4-Solution...

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ELEC210 Spring 2011 Homework-4-Solution 1. The random variable X has cdf as shown in the figure below: (a) What type of random variable is X? (b) Find the following probabilities: , , , , , . Solution(16 ): (a) (4 ) The cdf is neither continuous nor piece-wise constant, so it s mixed type. (b) (12 ) , , , , , . 2. A point is selected at random inside a square defined by . Assume the point is equally likely to fall anywhere in the square. Let the random variable Z be given by the minimum of the two coordinates of the point. (a) Find the sample space S of the coordinates of the point and the sample space of Z, . (b) Show the mapping from S to . (c) Find the region in the square corresponding to the event . (d) Find the cdf of Z. (e) Use the cdf to find: .

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Solution(16 ): (a) (3 ) , . (b) (3 ) The two segments as shown by the bold black curve in S correspond to point a in (c) (3 ) The region corresponding to the event is shown by the blue area. (d) (3 ) . (e) (4 ) , , , .
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