Question: Consider the following two random variables: X = 3 w/prob 1 3 2 w/prob 1 3 1 w/prob 1 3 Y = 30 w/prob 1

Consider the following two random variables: X = 3 w/prob 1 3 2 w/prob 1 3 1 w/prob 1 3 Y = 30 w/prob 1 3 20 w/prob 1 3 10 w/prob 1 3 (a) Y is a scaled version of X. Do X and Y have the same variance? (b) Intuitively, if we think of X as representing measurements in seconds, and Y as representing measurements in tenths of seconds, then we would like to feel that X and Y have the same variance. A common metric in computer systems is the squared coefficient of variation, where the squared coefficient of variation of X is written as C2 X and is defined as CX2 = Var E[X(X]2) . This can be viewed as a normalized variance. How do C2 X and CY2 compare?

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