It looks like ##\pi## just represents the parameter of the distribution. So this is not the common definition ##\pi = 3.14##... In the Bernoulli and Binomial cases, ##\pi## is the probability of success, and in the Poisson example, ##\pi## is the average rate of occurrence.zak100 said:
zak100 said:
It's the probability that a discrete random variable Y (with an assumed distribution) has the value y, given that the parameter of the distribution is ##\pi##.zak100 said:
The Bernoulli distribution is a discrete probability distribution that models the outcomes of a single trial of a binary event, where the outcomes are either success or failure. It is named after Swiss mathematician Jacob Bernoulli.
The Binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials of a binary event. It is derived from the Bernoulli distribution and is named after Swiss mathematician Jacob Bernoulli's father, Johann Bernoulli.
The Poisson distribution is a discrete probability distribution that models the number of events that occur in a fixed interval of time or space, given that these events occur at a constant rate and are independent of each other. It is named after French mathematician Siméon Denis Poisson.
Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. Pi is not directly related to these distributions, but it is often used in their formulas and calculations.
The Bernoulli, Binomial, and Poisson distributions are commonly used in statistics and probability to model various real-world phenomena such as coin tosses, disease outbreaks, and customer arrivals. They are also used in fields such as finance, engineering, and biology to make predictions and analyze data.
