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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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