# Search results

1. ### Integral with exponential terms?

I am doing some analysis and I have come up with the following integral: \int \frac{e^{-ax}}{1+be^{-cx}}dx where a>0, b>0 and c>0. I have found out this integral has a solution in terms of the Gaussian hypergeometric function http://en.wikipedia.org/wiki/Hypergeometric_function but it...
2. ### Kurtosis/4th central moment in terms of mean and variance

Hi All, Is it possible to express the kurtosis \kappa, or the 4th central moment \mu_4, of a random variable X in terms of its mean \mu = E(X) and variance \sigma^2 = Var(X) only, without having to particularize to any distribution? I mean, an expression like \kappa = f(\mu, \sigma^2) or \mu_4...
3. ### Simulation of beta-binomial distribution

Hi all! I'm trying to solve the following problem. The number of successes in a sequence of N yes/no experiments (i.e., N Bernoulli trials), each of which yields success with probability p, is given by the well-known binomial distribution. This is true if the success probability p is...
4. ### Integral of this exponential function: does it have a solution?

Hi all, I'm trying to solve the definite integral between 0 and inf of: exp(a*x^2 + b*x + c) --------------------- dx 1 + exp(m*x + n) with a,b,c,m,n real numbers and a < 0 (negative number so it converges). I've read in the forum's rules that I have to post the work that I have...