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Unformatted text preview: {9 ,8 ,..., 8 , 9 } (i.e. P ( X = k ) = 1 / 19 for9 ≤ k ≤ 9.) Problem 1 . Find P ( X 2 ≤ 5). Solution . P ( X 2 ≤ 5) = P (√ 5 ≤ X ≤ √ 5) = P ( X ∈ {2 ,1 , , 1 , 2 } ) = 5 / 19. Function of random variable discrete case Example. Let X be uniform on the 19 integers {9 ,8 ,..., 8 , 9 } (i.e. P ( X = k ) = 1 / 19 for9 ≤ k ≤ 9.) Problem 1 . Find P ( X 2 ≤ 5). Solution . P ( X 2 ≤ 5) = P (√ 5 ≤ X ≤ √ 5) = P ( X ∈ {2 ,1 , , 1 , 2 } ) = 5 / 19. Problem 2 . Find P (  X2  ≤ 5). Function of random variable discrete case Example. Let X be uniform on the 19 integers {9 ,8 ,..., 8 , 9 } (i.e. P ( X = k ) = 1 / 19 for9 ≤ k ≤ 9.) Problem 1 . Find P ( X 2 ≤ 5). Solution . P ( X 2 ≤ 5) = P (√ 5 ≤ X ≤ √ 5) = P ( X ∈ {2 ,1 , , 1 , 2 } ) = 5 / 19. Problem 2 . Find P (  X2  ≤ 5). Solution. P (  X2  ≤ 5) = P (5 ≤ X2 ≤ 5) = P (3 ≤ X ≤ 7) = 11 / 19....
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This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.
 Spring '10
 RohiniKumar

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