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  1. K

    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. K

    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."...
  3. K

    Books about Statistics

    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. K


    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. K

    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. K

    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. K

    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...