5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of X is 1. fx() = 6 a' a Var([X]), (b) Var(|X) > Var(X), and show the corresponding Var(X) and Var([X]), respectively, where [) represent rounding to the integer, i.e. [4.2] 4 and [5.6) = 6. %3D

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5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the
pdf of X is
1.
fx(#) 3=
6 - a'
a <a < b.
Give an example of a and b so that
(a) Var(X) > Var([X),
(b) Var(X) > Var(X),
and show the corresponding Var(X) and Var([X]), respectively, where [) represent rounding
to the integer, i.e. [4.2] = 4 and (5.6] = 6.
Transcribed Image Text:5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of X is 1. fx(#) 3= 6 - a' a <a < b. Give an example of a and b so that (a) Var(X) > Var([X), (b) Var(X) > Var(X), and show the corresponding Var(X) and Var([X]), respectively, where [) represent rounding to the integer, i.e. [4.2] = 4 and (5.6] = 6.
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