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January 29th, 2013, 12:14 AM   #1
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Weak Law of Large Numbers

Recall that . Hence, by using a uniform(0,1) generator, apprximate log 2. Obtain an error of estimation in terms of a large sample 95% confidence interval. If you have access to the statistical package R, write an R function for the estimate and the error of estimation. Obtain your estimate for 10,000 simulations and compare it to the true value.

My answer:

Where f(x)=1, 0<x<1

And then I calculated log 2 from the calculator and got 0.6931471806

From R, I got 0.6920717

So, from the weak law of large numbers, we can see that the sample mean is approaching the actual mean as n gets larger.

My Question:

Is my answer correct? Can I use the calculator to approximate log 2? If I shouldn't be using it...the problem that I'm having is if I compute the expected value, I get log 2. So it doesn't really help much. Can anybody give me a hint if it is wrong? By the way, I know I didn't compute the confidence interval yet...but I'm just asking if this portion of the problem is correct.

Thanks in advance
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