Re: Problem 1.9
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How do you know that ? I think that is a problem in your proof that you assumed that the joint probability works with Problem 1.9(b) inequality. To proof (b) I went this way: 1. I used Markov Inequality 2. Problem 1.9(a) gave me this: , hence Using this the rest of the proof is quite nice to carry out. 
Re: Problem 1.9
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Re: Problem 1.9
Here's my take on Problem 1.9, part(b), which is following the same lines as the description of MaciekLeks above.
We have: Since is monotonically increasing in t. Also, is non negative for all t, implying Markov inequality holds: The last line being true since [math]x_n[\math] are independent. From there it directly follows that 
Re: Problem 1.9
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Actually I don't even know how to tackle it. I think I'll need a lot of handholding through this one because my math got really rusty since I left school (I'm 34). 
Re: Problem 1.9
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Re: Problem 1.9
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Re: Problem 1.9
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But now I'm stuck at (d). Directly substituting is probably wrong? Because can be simplified to the point where no logarithm appears (unless I made a really big mistake). 
Re: Problem 1.9
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I did end up getting by substituting for , but only after simplifying all the way down, until there is no more or , otherwise I get two powers of 2 with no obvious way to combine them. So now the remaining hurdle is to prove that . Yay 
Re: Problem 1.9
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