Poisson Distribution The general form of the pdf for the Poisson distribution is $$ f(x; \lambda) = \mathbb{P}(X = x) = \frac{\lambda^x e^{-\lambda}}{x!} $$ And in this instance we say that the R.V \(X \sim P(\lambda)\). PGF The Probability Generating function of a Poisson Distribution has the following form $$ \begin{aligned} \mathcal{G}_{X}(z) &= \sum_{k = 1}^{\infty} z^k\frac{\lambda^k e^{-\lambda}}{k!} \\ &= e^{-\lambda}\sum_{k = 1}^{\infty} \frac{(\lambda z)^{k}}{k!} \\ &= e^{-\lambda}e^{\lambda z} \\ &= e^{\lambda(z - 1)} \end{aligned} $$

Honours Thesis This short post contains links to my honours thesis and honours presentation. The topic of my thesis was to create a computational structure for a semi-parametric vector generalized linear model. This was based on the earlier work of my supervisor, who had built up the theoretical framework for this model over a series of papers with other collaborators. Papers https://www.tandfonline.com/doi/abs/10.1080/01621459.2013.824892 R Package for Univariate Case Univariate model R package CRAN Link Relevant Links The following links contain some of my work on this topic.

Introduction In this very short blog post I want to go through the derivation of the quadratic equation as a simple teaching exercise. As most of us are aware from high school, when solving for the solutions to the following equation $$ ax^2 + bx + c = 0,\qquad a \neq 0 $$ one can use the quadratic equation, which has the general form. $$ x_{1, 2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$