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