# a1 - Independence Please hand in and 26 in Section 1.7 of...

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Math 471: Homework 1 Due Friday, September 5, 2008 Please remember that expressing your reasoning or proof clearly is very im- portant! You may discuss problems with other students but your writeups of homework must be your own. Homework is generally due in class or by class time under Dr. Back’s oﬃce door. Please read Chapter 1 and the ﬁrst two sections of Chapter 2 in EPFA. Sections 1.3-1.7 introduce a few deﬁnitions, but mostly preview a number of important topics we will work with much more intensively later in the course. So read them in this spirit. Basic Deﬁnitions Please hand in: problems 7 and 16 in Section 1.7 of EPFA . Please also look at problems 2, 4, 8, 10, and 18.
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Unformatted text preview: Independence Please hand in: problems 20, 23, and 26 in Section 1.7 of EPFA . Please also look at problems 19, 31, 33, and 34. Distributions, Expectation, and Variance Please hand in: problems 38, 54, and 55 in Section 1.7 of EPFA . Please also look at problems 35 and 39. Extra Problems 1. Set subtraction A-B is deﬁned by A-B = A ∩ B c . Prove that if B ⊂ A , then A = B ∪ ( A-B ) and P ( A-B ) = P ( A )-P ( B ) . Remark: A good way to prove equality of sets C = D is to show C ⊂ D and D ⊂ C . And to show C ⊂ D , one might start with x ∈ C and show x ∈ D as well. 2. Show that P ( A ∩ B ) ≥ P ( A ) + P ( B )-1 ....
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