Juan Esteban Betancur Isabella Shaikh Gabriela Morales Nicole Duque Daniela Caballero Angelica Balanta

In this R script, we demonstrate the distribution of the sample average of an exponentially distributed random variable resembles the normal distribution.

In this R script, we test to see if a continuously distributed random variable is normally distributed. Typically, empirical observations need not follow a specific distribution, so we need to conduct statistical test to see what is the most likely distribution. Experimentally, we sample from an exponential and normal distribution and perform the Shapiro-Wilk test (useful for low samples - KS test for large samples) to test for normality.

A demonstration of Step-Wise regression.

In this R script, we illustrate the heterogeneity of the posterior distribution using a Dirichlet prior for the multinomial distribution. We display Bayesian conjugacy plots that display the variability of prior and posterior distributions in the form of a contour plot.

In this R script, we explore the finite difference equation known as the logistic equation. We compute the trajectories for various parameter values of r and plot the steady states as a function of r and plot the last 400 of the 1200 time points. The result is a bifurcation map that displays a period-doubling bifurcation along with a region of chaotic oscillations (unpredictable).