Site icon Machine Learning For Analytics

Discrete Uniform Probability Distribution with MS-Excel

Hi ML enthusiasts! In our last post, we talked about basics of random variables, probability distributions and its types and how to generate a discrete probability distribution plot. In this article, we will talk about the Discrete Uniform Probability Distribution and its implementation with MS-Excel.

Discrete Uniform Probability Function

Consider the experiment of rolling a die. We have six possible outcomes in this case: 1, 2, 3, 4, 5, 6. Each outcome has equal chance of occurrence. Thus, the probability of getting a particular outcome is same, i.e., 1/6.

Consider the experiment of tossing a coin. We can have only two outcomes, Head and Tail. Also, for an unbiased coin, the probability of occurrence of each outcome is same, i.e., 1/2.

For an experiment having equally-likely outcomes and the number of outcomes being n, the probability of occurrence of each outcome becomes 1/n.

Thus, for uniform probability function, f(x) = 1/n.

Implementation using MS-Excel

Let’s see how to implement uniform probability distribution in MS-Excel now. Here, consider the case of rolling two dice. In this case, we get the following as outcomes:

(1,1), (1,2), …, (1,6), (2,1), (2,2), …, (2,6), (3,1), (3,2), …, (3,6), (4,1), (4,2), …, (4,6), (5,1), (5,2), …, (5,6), (6,1), (6,2), …, (6,6).

In this way, we get 6*6 = 36 outcomes. Since, the dice are unbiased, the outcomes will be equally likely. Thus, the probability of each outcome will be 1/36.

You can make the same type of distribution curves with any experiment that produces equally-likely outcomes and have no bias in it. For example, tossing two coins, estimating the likelihood of drawing a particular card from a deck of cards etc. All of these are the examples which generate the uniform probability distributions. Since the data points are discrete in nature, the probability distribution curve will also be discrete.

So, with this we conclude our tutorial. In the next tutorial, we will talk about the concept of expected value, standard deviation, variance and binomial probability distribution. Stay tuned!

Exit mobile version