The Maxwell's equations, are differential equations and no laws in the true sense. People just don't seem to get that!?
On the other hand, the Lorentz force law, the Coulomb's law, the Biot-Savart's law, the Faraday's law of induction as well as the conservation of charge are the fundamental...
Homework Statement
Consider a standard i.i.d. Gaussian random vector \mathbf{X} = [X_1 \cdot \cdot \cdot X_n]^T and its squared magnitude
||\mathbf{X}||^2 = \sum_{i = 1}^nX_i^2.
According to my textbook, to derive the density function of a chi-square random variable ||\mathbf{X}||^2 , one...
According to my textbook, to derive the chi-square density function, one should perform three steps. First we consider a standard i.i.d. Gaussian random vector \mathbf{X} = [X_1 \cdot \cdot \cdot X_n]^T and its squared magnitude
||\mathbf{X}||^2 = \sum_{i = 1}^nX_i^2.
1. For n = 1, show that...
I was on that track before, make use of the CDF and then differentiate back to get the PDF. This is how far I get: Let Y be a standard i.i.d. Gaussian vector. Then use the transformation
\mathbf{X} = \mathbf{A}\mathbf{Y} + \mathbf{\mu}
P(\mathbf{X} < \mathbf{x}) =...
If the covariance matrix \mathbf{\Sigma} of the multivariate normal distribution is invertible one can derive the density function:
f(x_1,...,x_n) = f(\mathbf{x}) =...