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Unformatted text preview: Math 151, Spring 2011
Jo Hardin, HW #11
Homework due on Thursday, April 7th , start of class.
1. DeGroot (3rd or 4th ed.), section 4.4: # 3, 4, 6, 9, 12
2. DeGroot (3rd or 4th ed.), section 4.6: # 3, 5, 6, 10
3. Let X and Y be identically distributed independent random variables such that the
mgf of X+Y is:
M (t) = 0.09e−2t + 0.24e−t + 0.34 + 0.24et + 0.09e2t −∞<t<∞ Calculate P (X ≤ 0).
4. We can show that for Y = g (X ) (some nonlinear function)
12
E (Y ) ≈ g (µX ) + σx g (µX )
2
(through a Taylor series expansion of g about µX ).
√
Let Y = g (X ) = X , and consider two cases: X ∼ U nif (0, 1) and X ∼ U nif (1, 2).
(Note: you can look up the mean and variance of a uniform in the back cover of your
book.)
For which distribution is the approximation better? Explain. ...
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This note was uploaded on 02/17/2012 for the course MATH 151 taught by Professor Jo.h during the Spring '10 term at Pomona College.
 Spring '10
 JO.H
 Math, Probability

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