Does Poisson distribution arise from the binomial distribution? You can find out in Lesson 37.

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# Poisson distribution Part 2

# Poisson distribution

# There’s nothing negative about the Negative Binomial distribution

# What is Return Period

# Geometric distribution and its basics

# Binomial Distribution Explained

# Bernoulli trials: the essential things to know

# Recap

# Playing large number games in R

# Standardizing the data

Does Poisson distribution arise from the binomial distribution? You can find out in Lesson 37.

*If you find this useful, please like, share and subscribe.*

*You can also follow me on Twitter **@realDevineni** for updates on new lessons.*

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.

In lesson 35, we learn the basics of the Negative Binomial distribution.

Lesson 35 – Trials to ‘r’th success: The language of Negative Binomial distribution

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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.

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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

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

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.

Why I created data analysis classroom? What did we learn so far? Where do we go from here? Find the answers in lesson 30.

I show you some simple tricks in R to simulate large number games using three examples.

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.