Coin tossing exercises are a simple but valuable means to understand a lot of real-life situations. Here we learn Poisson distribution by tossing a coin.
Poisson processes are used to model the number of occurrences of events over certain periods of time. They are discrete processes and also stochastic, i.e. the outcomes are random.
Customer arriving at a shop is often viewed as an example of the Poisson process. The shopkeeper knows the number of customers she expects in a day or an hour based on experience but never can’t predict what happens next minute. The following set of plots describes four such distributions for different mean arrivals (lambda).
As you can see, mean arrivals, coinciding with the peaks of these plots, are informative. However, the actual comings will vary between higher and lower values making certain decisions, staff allocations to support customers, for instance, very tricky.
So far, we have focussed on fixed time duration but random arrivals. You can also understand Poisson differently – a specified number of arrivals at random intervals. Look at the following graph: it describes a Poisson activity; time on the x-axis, and each vertical line denotes one appearance. Don’t waste your time on a pattern; there is no pattern!
Toss a coin
The above picture describes the tossing of a coin (e.g. every second) and marking an entry whenever a head happens.
n <- 100000
xx_f <- sample(c("H", "T"), n, TRUE, prob = c(1/2, 1/2))
index <- which(xx_f =="H")We just plotted the index values corresponding to H.
