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# tuto.04 - ENGG2430C Tutorial 4 Discrete Random Variable...

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ENGG2430C Tutorial 4 Discrete Random Variable, Expectation, and Variance Department of Information Engineering The Chinese University of Hong Kong February 12, 2013 ENGG2430C tutorial 4 February 12, 2013 1 / 9

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Example 1: PMF Example Let X be a random variable that takes values from 0 to 9 with equal probability 1/10. (a) Find the PMF of the random variable Y = X mod ( 3 ) . (b) Find the PMF of the random variable Y = 5 mod ( X + 1 ) . ENGG2430C tutorial 4 February 12, 2013 2 / 9
Example 1: PMF Solution : Using the formula p Y ( y ) = { x | x mod ( 3 )= y } p X ( x ) , we obtain p Y ( 0 ) = p X ( 0 )+ p X ( 3 )+ p X ( 6 )+ p X ( 9 ) = 4 / 10 ; p Y ( 1 ) = p X ( 1 )+ p X ( 4 )+ p X ( 7 ) = 3 / 10 ; p Y ( 2 ) = p X ( 2 )+ p X ( 5 )+ p X ( 8 ) = 3 / 10 ; p Y ( y ) = 0 , if y / ∈ { 0 , 1 , 2 } . Similarly, using the formula p y ( y ) = { x | 5 mod ( x + 1 )= y } p X ( x ) , we obtain p Y ( 0 ) = p X ( 0 )+ p X ( 4 ) = 2 / 10 ; p Y ( 1 ) = p X ( 1 )+ p X ( 3 ) = 2 / 10 ; p Y ( 2 ) = p X ( 2 ) = 1 / 10 ; p Y ( 5 ) = 5 / 10 ; p Y ( y ) = 0 , if y / ∈ { 0 , 1 , 2 , 5 } . ENGG2430C tutorial 4 February 12, 2013 3 / 9

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Example 2: Function of R.V. Example Let K be a random variable that takes, the integer values in the interval [ - n , n ] , with equal probability 1 / ( 2 n + 1 ) . Find the PMF of the random
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