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  1. J

    Deriving the chi-square density function

    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...
  2. J

    Deriving of the chi-square density function

    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...
  3. J

    How to derive the multivariate normal distribution

    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}) =...
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