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Unformatted text preview: cumulative distribution function, which is
0, , 0
1, (a)
(b)
(c)
(d) [4’] Find out the coefficient ;
[4’] Find the probability density function of ;
[4’] Find the probability that
0.1, 0.4 ;
[4’] Given we know that
0.5, find the probability that
4 0
1
1 0.1, 0.4 ; (e) [4’] Find the expected value and the variance of
Solution:
(a) Since
is continuous,
quantity, therefore
1
(b) By differentiating 1
1 4’ ; 1 . 1, where , we can obtain the following probability density function,
2 1,
0 1 , (c) 0.1 (d) Since 0.1 0.5
0.4 1 (e) 0.16 0.25, therefore
0.1
0.5 1 2 0.5 0.01 1 0.4 1
0.5 1 0.15 0.1...
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This document was uploaded on 03/19/2014.
 Fall '14

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