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in need of help for my statistics class


RobertGoulet

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You can also do what many modern scientists do when there isnt the data you need.

you can always make it up!

yea i think thats what im gonna have to do. i do appreciate u trying to get ppl to participate but who wants to do statistics when there is politics to argue about!?

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  • 3 years later...

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Okay...i have to do this extra credit assignment by 11:45am today...any help is greatly appreciated. The answers dont have to be right, I just have to show an honest attempt at solving the problem.

You can use this Excel sheet to generate a random variable Xi that is drawn from the box |-9|-8|27|27 (often you will see an error message if you open the Excel sheet; for some reason a file path is inserted in the first column and I cannot avoid that; you can look at the formula and remove it and things should be fine; the first column uses the function "=rand()" to generate uniform random numbers. The second column uses the =vlookup("adjacent left column", "lookup table", 2,1) command to produce a random variable Xi that is drawn from the box |-9|-8|27|27|).

1. Monte Carlo histogram for Xi with 100, 1000, 10000 repetitions

* please generate the MC histograms

* please decribe what you see

* how do the MC histograms change with the number of repetitions?

* what do the MC histograms have to do with the probability histogram of Xi?

2. Random variables that are i.i.d. combinations of the underlying random variable Xi

* please define the following random variables:

o Z1 = h(X1,..Xn) : = X1+..+Xn

o Z2 = h(X1,..Xn) : = (X1+..+Xn)/n

o Z3 = h(X1,..Xn) : = X1*..*Xn

o Z4 = h(X1,..Xn) : = (X1*..*Xn)/n

o Z5 = h(X1,..Xn) : = X1(X2+..+Xn)

o Z6 = h(X1,..Xn) : = X1(X2+..+Xn)/n

* please generate MC histograms (set number of MC repetitions equal to 10000) for each of the 6 defined random variables when

o n = 25

o n = 100

o n = 1000

* please decribe what you see

* how do the MC histograms change with the number of observations n?

* please compare the Monte Carlo histograms of the 6 different random variables

3. Please relate your findings to the law of large numbers (LLN) and the central limit theorem (CLT)

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My question is this - how do I define the random variables in question 2? I am stumped. Please help me :)

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I think what it's asking is, say for Z1 and n=25, calculate X1+X2+X3 ... + X25 and do this 10,000 times, charting the results as a histogram. Repeat for n=100 and n=1000. And repeat for the calculations specified in Z2 through Z6.

But I don't know what the function Xi is to know if this makes sense.

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