Recent content by Gekko

The solution can be obtained form considering the first 1 to n-1 samples which must all be equally likely to be chosen This yields 1/n(n-1) * [sum from 1 to (n-1) (x^2 + (n-x)^2)] and has been verified. Can be simplified further. There must be another way to do this though? A more...

Homework Statement We choose two groups where group A can be of size X where X ranges from 1 to n-1. Group B is the remaining (n-X). All values of X are equally likely and all group sizes are equally likely If we choose one item from 1 to n where all choices are equally likely, what is...

I see. Understood. Thanks a lot for taking the time to answer my questions. Appreciate it

Actually, no the answer is here http://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables So something isn't working out in both the exponential (should be dividing by 2(1+p)) and the coefficient in front of the exponential (should be 1/sqrt(2pi))

Hi Lanedance Integrating the final part wrt x gives: sqrt(pi)/sqrt(2p+2) * exp(-2(1+p)(z/2)^2) The sqrt(2p+2) is correct as the correlation component of the summation. Does the rest look OK?

Lanedance, Thanks for your replies. I believe what Statdad was referring to was the joint PDF of a bivariate distribution i.e. http://upload.wikimedia.org/math/b/1/0/b10ecc56f758b2f94a953e7e1bd2f1c2.png In proving that X+Y is normal and where X and Y are dependent, not sure how you ignored...

Thanks a lot for your replies. After making the substitution, there just isn't a way to minimize (completing the square or otherwise) because we have uv terms with different divisors. Is the approach rather to take u=x+y and v=something else? Is the choice of v the key? Has anyone actually ever...

Unfortunately this approach doesn't seem to work. I end up with a very messy exponential which doesn't allow separation for the marginal calculation :( Any thoughts? Is this not a standard proof?

If I change variables, U=X+Y and V=X-Y and take the jacobian, I can then take the marginal to find f_U. However, how do you change the standard deviation and means when you perform change of variables?

Homework Statement If X and Y have a bivariate normal distribution with correlation p, show that X +Y is normally distributed This seems like a pretty standard proof but can't find it anywhere. Simply adding the marginal distributions, X+Y is what I tried but how is the correlation...

Yes, that's not right I see. I used this approach instead. To find the first moment of a uniform distribution it is: 1/(b-a) * integral from a to b of x In this case it is 1/(b-a) * integral from a to b of ln(x) Is this ok? This approach calculates the correct value for...

Homework Statement How to calculate the expected value of the log of a uniform distribution? Homework Equations E[X] where X=ln(U(0,1)) The Attempt at a Solution integral from 0 to 1 of a.ln(a) da where a = U(0,1) = -1/4 However I know the answer is -1

As n tends to infinity, the cumulative distribution function Fk(Xk) tends to F(X) I think this is ok. I don't see how to show this tends to a normal distribution though. I think I'm making this much harder than it is. Don't see anything close in any textbook or on the web!

I looked at taking the mgf thinking if I can show the mean to be 0 and variance 1 from this approach and hence prove normality g(t) = 1(1/sqrt(n) sum(from 1 to inf) exp(tk) [1+log(1-Fk(Xk))] but this approach goes nowhere

No, there is a cdf for each x. Fk(xk) for k=1 to n F1(x1), F2(x2) etc Sorry, it's the lack of latex that makes it hard to show subscript