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Discrete Probability Distributions

Discrete Probability Distributions

Hi ML Enthusiasts! Today, we will talk about discrete probability distributions and their implementation in MS-Excel. This is very important as it lays the foundation of statistics which is very useful if you want your career in Data Science.

So, let’s start with our tutorial!

Random Variables and their Types

Every experiment that we do has its associated outcomes. For example, tossing a coin has two outcomes, head and tail. Similarly, rolling a die has six outcomes, 1, 2, 3, 4, 5 and 6 dots. These outcomes are required to be defined using numerical values. This requirement is solved by using random variables.

Random variables serve the purpose of defining the experimental outcomes using numerical values. These numerical values can be discrete or continuous depending upon their properties. When the values the random variable takes have definable infinite range or gap or are finite in nature, such as 1, 2, 3, 4, …, n, it is called as discrete random variable. When the values do not have any definable range or gap, it is called as continuous random variable.

An example of discrete random variable is number of cars sold per day in a particular showroom. This random variable can take values such as 1, 2, 3, or more depending upon the number of cars sold per day. Also, there is a fixed gap between two numbers (2 – 1 = 4 – 3= 1). An example of continuous random variable is the values of temperature recorded after every one hour each day. For example, 22.6ºC, 26.44ºC etc.

Concept of Probability Distributions

Every value of random variable has a probability (likelihood of occurrence) associated with it. We define the probability distribution as the description of how the probabilities are distributed over the different values the random variable takes.

Let the random variable be x. We define the probability function of x as f(x). f(x) provides the curve of variation of probabilities with variation of x. For example, f(0) provides the probability of selling 0 cars per day, f(3) provides the probability of selling 3 cars per day. Likewise, f(0ºC) provides the probability that the temperature is 0ºC per hour.

Discrete Probability Distributions

When the random variable in consideration is discrete in nature, the probability distribution also comes out to be discrete. The required condition associated with it are as follows:

1 ≥ f(x) ≥ 0 and ∑f(x) = 1.

We can carry out following observations from these two equations:

Implementation using MS-Excel

Now let’s learn how to analyse a discrete probability distribution on Excel.

Let’s consider a situation in which we are given the data of number of cars sold per month by a showroom and we need to come out with the probability distribution of this data.

RAND function in Excel

Int function

Sum function

Fetching probability of each outcome

Building discrete probability distributions

With this, we conclude our tutorial. We will talk about different types of discrete probability distributions in our next tutorial. So, stay tuned in this excel series.




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