Recent content by Kiuhnm

1. cross term

The book says that the following cross term can be shown to be zero by iterating the expectation: E[(Y-E(Y|X))(E(Y|X)-g(X))]. What does it mean "to iterate the expectation"?
2. mean and variance of a beta distribution

I'm trying to do point (b) of exercise 3.30 of the book "Statistical Inference" (Casella & Berger). The exercise says: "Use the identities of Theorem 3.4.2. to (a) calculate the variance of a binomial random variable. (b) calculate the mean and variance of a beta(a,b) random variable."...

I took a course in Statistics years ago (first year of university), then I studied the book of Rice on my own. After that, I tried to read graduate level books about Machine Learning, but found my knowledge in probability and statistics insufficient. I want to really understand statistics. I'm...
4. cumulants

I don't know much about cumulants. What I know is that they can be generated by using the cumulant generating function g(t) = \log(E[\exp(tX)]). I'm studying the so-called Independent Component Analysis and my book says that if the pdfs involved are symmetric then the odd order cumulants are...
5. Multivariate gaussian, MLE

How do you take the derivative of \ln p(X|\mu,\Sigma)=-\frac{N D}{2}\ln(2\pi)-\frac{N}{2}\ln|\Sigma|-\frac{1}{2}\sum_{n=1}^N(x_n-\mu)^T\Sigma^{-1}(x_n-\mu) with respect to \Sigma?
6. Dirichlet distribution

I computed mean, variance and covariance of the Dirichlet distribution. To do so, I computed E[x_k], E[x_k^2] and E[x_i x_j]. This is the first time I've dealt with multivariate distributions. The mean should be the weighted sum of the vectors x in the simplex so I can consider one component at...
7. Poisson process in 3D

I haven't the slightest idea of how to tackle the following problem. Find the probability density for the distance from an event to its nearest neighbor for a Poisson process in three-dimensional space. All my book says about "Poisson processes" is "The Poisson distribution often arises...