Introduction
Bernoulli’s process is under the statistics field of mathematics and is centered on the binary level and sequences. Typically, a Bernoulli process consists of an infinite or finite sequence of random variables that take binary values. It implies that they can only take two values, either zero or 1 (Lee, 2021). The essay describes an event in one’s life that fits the characteristics of a Bernoulli process, explaining how each property is fulfilled by the event in life and the number of trials and successes for the event.
Properties of Bernoulli Process
The characteristics of a binomial experiment comprise:
- an experiment that includes a series of n identical trials,
- two results are possible on every trial, in which one should be labeled success and another result as a failure.
- The possibility of success cannot change from trial to trial and is termed as p.
Consequently, the possibility of a failure cannot alter from trial to trial and is termed as 1-p (Erazo & Goldsman, 2021). However, these trials are independent of each other during an experiment.
An Example of a Real-Life Event
A binomial distribution example that I consider fits this Bernoulli process is purchasing a lottery ticket. There are two outcomes here: losing or winning in the trials. You are going to purchase a lottery ticket and either lose or win. Therefore, if one buys a ticket, the variables are either losing or winning. For instance, in one month, I bought 16 tickets and won four times, implying I won 25 percent of the time during the month.
Conclusion
Bernoulli distribution presents two results, either a failure or a success in any trial. This implies that the number of trials within a binomial distribution is n=1. Hence, the results of a binomial experiment match a binomial probability distribution. A life event applied in this case, such as trying to get a baby through pregnancy, is considered to be a Bernoulli distribution because it is either having a child or a miscarriage.
References
Erazo, I., & Goldsman, D. (2021). Efficient confidence intervals for the difference of two Bernoulli distributions’ success parameters. Journal of Simulation, 17(1), 76-93. Web.
Lee, J. (2021). Generalized Bernoulli process with long-range dependence and fractional binomial distribution. Dependence Modeling, 9(1), 1-12. Web.