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hw3 - Stat 310A/Math 230A Theory of Probability Homework 3...

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Stat 310A/Math 230A Theory of Probability Homework 3 Andrea Montanari Due on 10/14/2009 Solutions should be complete and concisely written. Please, use a separate sheet (or set of sheets) per each problem. Staple sheets referring to the same problem, and write your name on each sheet. You are welcome to discuss problems with your colleagues, but should write and submit your own solution. In some cases, multiple homework options will be proposed (and indicated as ‘Option 1’, ‘Option 2’, etc.). You are welcome to work on all the problems proposed (solutions will be posted), but should submit only those corresponding to one ‘Option’. Exercises on inequalities and convergence Solve Exercises [1.3.21], [1.3.36], [1.3.37] from Amir Dembo’s lecture notes. Exercises on L p spaces Fix a probability space (Ω , F , P ). Throughout this exercise, we will say that two random variables X , Y are equivalent if { ω : X ( ω ) 6 = Y ( ω ) } ⊆ Ω 0 for some Ω 0 ∈ F with P 0 ) = 0.
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