Tuto.04

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Unformatted text preview: ([email protected]) ENGG2430C tutorial 4 February 12, 2013 3/9 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/(2n + 1). Find the PMF of the random variable Y = ln X , where X = a|K | , and a is a positive number. ([email protected]) ENGG2430C tutorial 4 February 12, 2013 4/9 Example 2: Function of R.V. Solution: Y = ln X = |K | ln a. Thus, we 2n2 1 , + pY (y ) = 2n1 1 , + 0, ([email protected]) have if y = ln a, 2 ln a, . . . , n ln a, if y = 0, otherwise. ENGG2430C tutorial 4 February 12, 2013 5/9 Example 3: Expectation and Variance Example Let X be a random variable with PMF pX (x ) = x 2 /a, if x = ±3, ±2, ±1, 0, 0, otherwise. (a) Find the scalar a and E[X ]. (b) What is the PMF of the random variable Z = (X − E[X ])2 ? (c) Using the result from part (b), find the variance of X . ([email protected]..
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This test prep was uploaded on 03/31/2014 for the course ENGG 2430C at The Chinese University of Hong Kong.

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