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Unformatted text preview: Solutions to Homework 05 1. a. Yes, because: the function is nondecreasing, F X ( ) = 0 and F X ( ) = 1. b. No, because F X ( ) = 0 . 9 6 = 1. c. No because the function is not nondecreasing (there is a decrease at x = 2). 2. a. The sample space is described by the sum of the coordinates of the points hit by the dart. The smallest sum is 0 when the x and y coordinates are { , } i.e. the dart hits the lower left corner of the square. The largest sum is 2 b when the dart hits the upper right corner whose coordinates are { b, b } . Then, the sample space is given by S Z = { z : 0 z 2 b } . b. There can be two possible shapes for the region depending on the value of z . Students get full points even if they show one. The regions are shown in Figure 1. x y y=zx b b z z x y b b y=zx (a) Case 1: 0 < z < b (b) Case 2: b < z < 2 b Figure 1: The region in the square corresponding to the event { Z z } for < z < ....
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 Fall '08
 GELFAND

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