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Speeding Cars and Mixed Distributions

Jadon Jones ⟨jadon.jones@vikings.berry.edu⟩

Abstract:

In this project, we model the time advantage of speeding on a highway with traffic lights as a stochastic process. The object of study is the sequence of random variables Tk, representing the time benefit of the speeding car at the k th traffic light. For simplicity, we assume identical traffic light cycles with independently distributed initial phases and constant distance between lights. With this simplified model, we investigate the distribution of Tk, proving results on the expected value of Tk and deriving the conditional distribution Tk|Tk1. The first result gives some intuition on the situation being modeled and the second result shows that Tk|Tk1 and thus Tk are examples of mixed distributions. Though the model serves more as a toy model, it provides an interesting example of a family of distributions having both a continuous and discrete part that arises from a simple mathematical model.

Scheduled for: 2025-03-01 10:45 AM: Undergraduate Poster Session #12 in Phillips Lobby

Status: Accepted

Collection: Undergraduate Posters

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