To further our understanding of the evolution of the universe, particularly the distribution of dark matter creating the cosmic web of galaxies and clusters, we need to determine distances to galaxies. The peak luminosities of Type Ia supernovae can be determined from their consistent light curves. Therefore, analysis of Type Ia supernovae within galaxies results in estimates of the distance modulus, a parameter that can be used to determine the distance of a supernova and its host galaxy. This estimate is impacted by the environment of a given supernova. Characterization of hosts thus allows for environmental adjustments to be made to improve the estimate of the distance moduli. In this project, we have determined candidate galaxies for observation with the Green Bank Telescope by crossmatching supernovae from the Democratic Sample of Supernovae (DSS, Stahl et al. 2021) to host galaxies using the Open Supernova Catalog, NASA/IPAC Extragalactic Database, and the Arecibo General Catalog. Information such as luminosity, flux, and position were used to construct the presented candidate list. The observation run will result in the characterization of host galaxies through future analysis of radio emission of neutral hydrogen and data from other observing bands available in digital catalogs of galaxies.

The Gaussian (aka normal) probability distribution is a tool of tremendous importance for the statistical analysis of data from many fields. We explore its derivation and investigate the generalization from the univariate to the bivariate case. With these foundations in place, Gaussian Process Regression is defined and basic properties discussed, including modelling considerations. We implement the method in the R programming language for the analysis of education data, and discuss the results in comparison with traditional regression techniques.

How does the lottery drawing system work? Is it true that the winning numbers, as well as each individual digit, were chosen at random? This project uses R Studio to investigate two of New York’s most popular lottery drawing games to see if the numbers picked are as random as the Lottery Commission claims. This was achieved by applying Chi-Square of Goodness test to determine p-values and identify whether or not there is evidence that the numbers are not drawn randomly. The data utilized to investigate the distribution of winning numbers is the winning numbers for the New York Daily Numbers and Win 4 since the 1980’s. The Daily Numbers are three-digit numbers drawn between 000 and 999, whereas the Win 4 numbers are four-digit numbers drawn between 0000 and 9999. The numbers are drawn one digit at a time, so we are investigating the numbers as both 3 (respectively 4) digit numbers, and the individual digits. Along with determining whether the probability of winning is equally distributed, the expected value was also calculated to assess whether playing is worth it.