Recent content by autobot.d

Want to understand a concept here about dimensions of a function. Using example 1: a simple Fourier series from http://en.wikipedia.org/wiki/Fourier_series s(x) = \frac{a_0}{2} + \sum ^{\infty}_{0}[a_n cos(nx) + b_n sin(nx)] So do we now say that s(x) has an infinite dimensional...

so for "f0 probability that 0 X_i are added", and assuming f0 = {0 \choose n}p^0(1-p)^{n}=(1-p)^n and so on, then what do I do with all the f0, f1, ... is the average like a weighted average pretty lost so any help is greatly appreciated. Thanks.

But what about the fact that the m in the summation limit is Binomially distributed? I do not understand what that does? Thanks.

What kind of problem is this? X_i \textrm{are iid with known mean and variance, } \mu \textrm{ and } \sigma ^2 \textrm{respectively. } m \sim \textrm{Binomial(n,p), n is known.} S = \sum^{m}_{i=1} X_i How do I work with this? This what I have thought of. S = \sum^{m}_{i=1} X_i =...

Is there a reference you could point me to or a reason why? Would it be true if \mu > \hat{\mu} and for \mu < \hat{\mu} E[|\mu - \hat{\mu}|] = \frac{2}{\sqrt{\pi}} by going through and doing the actual integration.

Awesome, I end up with the same answer as before. Thanks for the help.

I think this is right. \frac{d}{d \sigma ^2} [log(\sigma ^2) - \frac{1}{\sigma ^2}] = \frac{1}{\sigma ^2} + \frac{1}{\sigma ^4} then for the second derivative \frac{d}{d \sigma ^2} [\frac{1}{\sigma ^2} + \frac{1}{\sigma ^4}] = - \frac{1}{\sigma ^4} - \frac{2}{\sigma ^6} Yay...

\frac{d}{d \sigma ^2} [log(\sigma ^ 2) - \frac{1}{\sigma ^ 2}] I think the first part is \frac{1}{\sigma ^ 2} but pretty clueless after that. I also want to take the second derivative. Any help or a reference would be great. Thanks!

Homework Statement X_{1} , ..., X_{5} \textit{ iid } N( \mu , 1) \textit{ and } \hat{\mu} = \bar{X} where L( \mu , \hat{\mu} ) = | \mu - \hat{\mu} | The Attempt at a Solution E[ | \mu - \hat{\mu} | ] = 0 since E(\hat{\mu}) = \mu Am I missing something? Seems too easy...

Homework Statement We have A \in R^{mxm} \text{ and } b \in R^{m} \text{ and } b \neq 0 \text{. Show that } Ax = b \text{ and } A(x+ \delta x) = b+ \delta b The Attempt at a Solution I did the first part just by the definition of A being non singular. The second part is tripping...

Makes sense it should be a function of w only. I do not understand though how the integral with the minimum is broken up into the two integrals at the end. Any insight? Thanks for the help.

Homework Statement Let x,y be iid and x, y \sim U(0,1) (uniform on the open set (0,1)) and let z = xy^2. Find the density of z. Homework Equations The Attempt at a Solution P(z \leq w) = P(xy^2 \leq w) = P(- \sqrt{\frac{w}{x}} \leq y \leq \sqrt{\frac{w}{x}}) = \int^{...

Homework Statement Z is a 2x1 multivariate gaussian random vector, where Z = (X Y)^t , X,Y are real numbers, with mean zero and covariance matrix \Gamma which is a 2x2 matrix whose entries are \Gamma_{1,1} = 1 \Gamma_{1,2} = \alpha \Gamma_{2,1} = \alpha \Gamma_{2,2} = 1...

They are the same X and Y values. 1 and 2 are totally separate. There is another question about conditional expectation that goes with 2. but I think I can get that part with a little help on 2. Thanks for the help.

Awesome, thanks for the help. Now where might a good reference be for my second problem. Is this thought process right? 1. Integrate Y to get the marginal of X to get F 2. Do convolution to get distribution of G = X+Y 3. How do I recover Joint distribution from marginals?