131A_1_hw5_solution

131A_1_hw5_solution - EE 131A Problem Set #5 Probabilities...

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Unformatted text preview: EE 131A Problem Set #5 Probabilities Instructor: Vwani Roychowdhury 1. Problem 3 . 4. (a) S Y = [0 , 1). (b) Its a circle (as well as its inside area) with its center at the origin, its radius as y . (c) P [ Y y ] = . 5 y 2 . 5 1 2 = y 2 . 2. Problem 3.15 (a) X is a r.v. of mixed type since it is continuous except for discontinuity at 0 and at 1. (b) P [ X <- . 5] = F X (- . 5- ) = 0 P [ X < 0] = F X (0- ) = 0 P [ X 0] = F X (0) = 0 . 25 P [0 . 25 X < 1] = F X (1- )- F X (0 . 25- ) = 3 16 P [0 . 25 X 1] = F X (1)- F X (0 . 25- ) = 11 16 P [ X > . 5] = 1- P [ X . 5] = 1- F X (0 . 5) = 5 8 P [ X 5] = 1- P [ X < 5] = 1- F X (5- ) = 0 P [ X < 5] = F X (5- ) = 1 3. Problem 3.15 (b). P [ k < Y k + 1] = F Y ( k + 1)- F Y ( k ) = (1 /k ) n- (1 / ( k + 1)) n 1 4. P [ R 2 ] = P [ < R 2 ] = F R (2 )- F R ( ) = e- . 5- e- 2 . P [ R > 3 ] = 1- P [ R 3 ] = 1- F R [ e ] = e- 9 / 2 5. Problem 3.23 F X ( x ) = Z x- f x...
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This note was uploaded on 03/27/2012 for the course EE EE 131A taught by Professor Roychowdhary during the Spring '05 term at UCLA.

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131A_1_hw5_solution - EE 131A Problem Set #5 Probabilities...

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