It is crucial to understand probability distributions in the data-driven Six Sigma approach. Probability distributions are a way to determine how likely an event will occur. Different data types will have different distributions. Why is this important? We learn in the Lean Six Sigma Course that probability distributions have an effect on the types of statistical tools that can be used to analyze this type of data. After you have completed a Lean Six Sigma training course and are ready to apply Six Sigma principles, you will need information about the type of probability distribution that is relevant to the data you have collected during the Six Sigma Measure phase.

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What is Probability?

Let’s first understand what probability is. The term “probability” means a likely or probable event. Probability is a measurement or estimation of the likelihood that something will happen or if a statement is true. Probabilities can be given a value between 0 (0, or not happening) and 1 (100% chance that it will happen). The probability of an event occurring is determined by how likely it is. If the sample is longer, the probability of such an event happening is also higher. In other words, the probability that an event will occur is the measure of how likely it is that it will.

How do you calculate probability?

The probability is calculated by dividing positive outcomes by the total number possible outcomes. The probability of a given outcome can be expressed as ‘f’ divided with ‘N. f refers to the number possible outcomes, while N refers to the number that are likely to be favorable.

These are the three basic properties of probability

These are the three basic properties that make up Probability:

Property 1: The probability that an event will occur is always between 0 & 1, inclusive

Property 2: The probability that an event will not occur is 0. Note that an event that is impossible to occur is called an impossible situation.

Property 3: The probability that an event will occur is 1. A certain event is an event that must happen.

A coin flip is the simplest example. There are only two outcomes when you flip a coin. The result is either heads, or tails. So the chance of getting heads is one out of two, or half (50%).

Definition of Probability Distribution

Probability distribution maps the likelihood of multiple outcomes within a table or equation. It is simply a table or equation that links each outcome in a statistical experiment to its probability of occurring. It is important to understand variables in order to fully grasp this concept.

Variables are symbols (A, B., x.y., etc.). A variable is a symbol (A, B, x, y etc.). It can take on any value from a set of values.

A random variable is a variable whose value is determined by a statistical experiment.

Statisticsians generally use a capital letter for random variables and a lower-case letter for different values.

X is the Random Variable “X”.

P(X), the Probability of “X”

P(X =x) is the probability that the random variable, X, equals a particular value denoted with ‘x’. For example, P (X = 1) is the probability that random variable X equals 1.

There are two types of probability distributions: continuous probability distribution or discrete probability distribution. We will be focusing on the latter.

Two types of probability distribution

What is discrete probability distribution?

A discrete probability distribution is a way to describe the probability of each value in a discrete random variables. A discrete random varible is one that has countable values. If the sum of all probabilities is one, the variable is considered random.

If a coin is to, for example,