Discrete Probability Distribution In Six Sigma – What It Is And How To Use It

It’s critical to grasp the notion of probability distributions when it comes to the data-driven Six Sigma methodology. Probability distributions inform us of how probable it is that something specific will happen. Different distributions exist for different kinds of data. But you might be wondering why we want this information?

Well, we learn in the Lean Six Sigma Course that probability distributions have an impact on the sorts of statistical techniques that are appropriate for that type of data. So, once you’ve completed a recognized Lean training program and are ready to use Six Sigma principles on your project’s DMAIC cycle, you’ll need to decide what sort of probability distribution applies to the information you obtained during the life of the Six Sigma Measure stage.

What Exactly Is Probability And How Do You Calculate It?

Let’s take a quick look at what the word probability entails. A likely or plausible event is commonly referred to as probability. Probability is the way to measure or estimate the likelihood of something occurring or that of a proposition being true. Probabilities are assigned a number between zero (zero percent likelihood) and one (100 percent chance that something will occur). The larger the probability, the more probable it is that the event will occur, or, in something like a lengthier series of samples, the higher the likelihood of times that such an occurrence will take place.

Essentially, an event’s probability is a measure of the likelihood that an outcome will happen as a consequence of a test.

The quantity of positive outcomes is divided by the complete amount of potential outcomes to compute the probability. The probability a certain event has of happening may be calculated by dividing ‘f’ by ‘N’. The letters ‘f’ and ‘N’ here stand for the number of favorable results and the number of conceivable possibilities, respectively.

The 3 Basic Properties Of Probability

There are 3 properties that you need to know about when it comes to probability. Here they are::

- Property No. 1: An event’s probability will always be between zero and one
- Property No. 2: An event that cannot happen has a probability of zero. Please keep in mind that an impossible occurrence is the name for something that cannot happen.
- Property No. 3: A must-happen event has a probability of one. A certain event is the name for an occurrence that has to happen.

If you need an example, taking a basic coin flip is one of the easiest ways to illustrate this concept. There are just 2 potential results when flipping a coin: heads and tails. As a result, the chance of landing on heads is one in two or 50 percent.

A Proper Definition For Probability Distribution

A probability distribution depicts the chance of many outcomes in an equation. Basically, it’s a table or even an equation that connects every statistical experiment’s result to the likelihood of it occurring. It’s crucial to comprehend the notion of factors in order to grasp this topic.

- Any character like x, y, and so on which can have a specific value is called a variable
- A variable whose value is determined by the results of a random experiment can be referred to as a random variable.

Usually, statisticians have been using a capital letter to denote a random variable and just a lowercase one to signify various values. Here is an example:

- A Random Variable will be represented by X.
- The probability of ‘X’ is represented by P(X).
- The chance that such a random variable is equivalent to a given value, represented by ‘x,’ is indicated by P(X = x). P(X = 1), for example, describes the probability of random variable X being equal to one.

Continuous probability distributions and discrete probability distributions are the two primary forms of probability distributions. In this Brain Sensei blog, we will only talk about the discrete probability distribution.

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Types of Probability Distribution: Discrete Probability Distribution

The likelihood of every value of a discrete random variable occurring is described by the term “discrete probability distribution”. A quantifiable arbitrary variable is commonly known as a discrete random variable. If the total of the odds equals one, the variable will be considered to be unpredictable.

For instance, if you throw a penny 3 times, the number of heads you get might be zero, one, two, or three. To put it another way, the resulting value of heads has just four possible outcomes: zero, one, two, or three, making the variable discrete. When it comes to a discrete probability distribution, receiving heads or tails, even if it’s just zero times, has a value.

Looking at this illustration, you can see that the total number of probabilities equals one. In the case of heads taking four values, then that means the number of tails can take four values as well. As a baseline value, the total sum is recorded, and as a consequence, the likely outcome is 1 by 8. Each potential value of the discrete random variable could be linked with a probability higher than zero in a discrete probability distribution. Therefore a discrete probability distribution is frequently depicted as a table.

Discrete Probability Distribution

- It explains the change of what could happen for each of the various values of a discrete random variable
- With discrete probability distribution, each potential number of the variable could be connected to a non-void possibility
- In the context of discrete variables, please have a look at the table below

Event: Tossing a coin three times

Number of heads |
0 |
1 |
2 |
3 |

Probability |
1/8 |
3/8 |
3/8 |
1/8 |

Non-Uniform Distribution

For further information on uniform probability distribution, see the illustration below. This is a very simple example to better help you understand the idea. It starts by throwing a dice. A die contains 6 sides, every one of them assigned a number from one to six, and every side has an identical chance of appearing when you roll it. A probability distribution, such as the uniform probability distribution chart in the picture, can be created to represent the chances of receiving any certain value on a single throw.

## Discrete Probability Distribution

Uniform Distribution

Resulting Number |
Probability |

1 |
1 out of 6 (⅙) |

2 |
1 out of 6 (⅙) |

3 |
1 out of 6 (⅙) |

4 |
1 out of 6 (⅙) |

5 |
1 out of 6 (⅙) |

6 |
1 out of 6 (⅙) |

None-Uniform Distribution

Resulting Number |
Probability |

1 |
One dot on 3 out of 6 sides Probability = 3 / 6 (50%) |

4 |
Four dots on 3 out of 6 sides Probability = 2 / 6 (33%) |

6 |
Six dots on 1 out of 6 sides Probability = 1 / 6 (17%) |

To further explain non-uniform probability distribution, let’s use the same example. We’ll need to suppose that we altered a die to be made of just 3 sides with one dot, 2 sides with four dots, and 1 side with six dots. So now there are 3 potential outcomes (one, four, and six), so the likelihood of receiving every single one of those numbers is varied. For a clearer visual example, take a look at the table in the image above.

What We Learned About Discrete Probability Distribution

In this Brain Sensei blog post we have learned about the binomial probability distribution and the poisson probability distribution, which are the two forms of discrete probability distribution. Although we didn’t touch on both of the discrete probability distributions in this article, they will be discussed in future blog posts. We hope this information was useful and helps you in being able to interpret your Six Sigma data in a more efficient way now that you know about discrete probability distribution.