Poisson distribution

If we assume events are independent (the occurrence of one event does not affect the probability that a second event will occur), then the counts per unit interval can be assumed a random variable that follows a probability distribution. Counts, i.e., the number of times an event occurs in an interval follows a Poisson distribution.

Poisson distribution has one control parameter. It is the rate of occurrence; the average number of events per unit interval.

In lesson 36, we learn the fundamentals of Poisson distribution. You will also meet Able and Mumble two of my friends.

Lesson 36 – Counts: The language of Poisson distribution

 

What is Return Period

Your recent vocabulary may include “100-year event” (happening more often), (drainage system designed for) “10-year storm,” and so on, courtesy mainstream media and news outlets.

Does a 10-year return period event occur diligently every ten years? Can a 100-year event occur three times in a row?

If we define T as a random variable that measures the time between the events (wait time or time to the next event or time to the first event since the previous event), the return period of the event is the expected value of T, i.e., E[T], its average measured over a large number of such occurrences.

In lesson 34, we learn about return period through Bob and his reappearance. Bob’s time of occurrence also relates to Geometric distribution.

Lesson 34 – I’ll be back: The language of Return Period

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Geometric distribution and its basics

Try, try and try again till you succeed. That is Geometric distribution.

If we consider independent Bernoulli trials of 0s and 1s with some probability of occurrence p and assume X to be a random variable that measures the number of trials it takes to see the first success, then, X is said to be Geometrically distributed.

In lesson 33, we learn the basics of Geometric distribution.

Lesson 33 – Trials to first success: The language of Geometric distribution

 

Binomial Distribution Explained

In lesson 31, we learned the idea of Bernoulli sequence. In lesson 32, we take this idea as the basis to understand Binomial distribution. When we are interested in the random variable that is the number of successes in so many trials, it follows a Binomial distribution. “Exactly k successes” is the language of Binomial distribution.

Full lesson here.

Lesson 32 – Exactly k successes: The language of Binomial distribution

 

 

Bernoulli trials: the essential things to know

There are two possibilities, a hit (event occurred — success) or miss (event did not occur — failure). A yes or a no. These events can be represented as a sequence of 0’s and 1’s called Bernoulli trials with a probability of occurrence of p. This probability is constant over all the trials, and the trials itself are assumed to be independent, i.e., the occurrence of one event does not influence the occurrence of the subsequent event.

In lesson 31, we discuss the fundamentals of Bernoulli trials. They form the basis for deriving several discrete probability distributions that we will learn over the next several weeks.

Lesson 31 – Yes or No: The language of Bernoulli trials

 

Standardizing the data

In this lesson, we learn about the basics of standardizing the data.

If our interest lies in working simultaneously with data that are on different scales or units, we can standardize them, so they are placed on the same level or footing. In other words, we will move the distributions from their original scales to a new common scale. This transformation will enable an easy way to work with data that are related, but not strictly comparable.

Lesson 28 – Apples and Oranges