Statistics How To

Discrete Probability Distribution: Definition & Examples

Probability Distributions > Discrete Probability Distribution

You may want to read this article first:
Discrete vs. Continuous Variables

What is a Discrete Probability Distribution?

In statistics, you’ll come across dozens of different types of probability distributions, like the binomial distribution, normal distribution and Poisson distribution. All of these distributions can be classified as either a continuous or a discrete probability distribution.
A discrete probability distribution is made up of discrete variables. Specifically, if a random variable is discrete, then it will have a discrete probability distribution.

Discrete Probability Distribution Examples

For example, let’s say you had the choice of playing two games of chance at a fair.
Game 1: Roll a die. If you roll a six, you win a prize.
Game 2: Guess the weight of the man. If you guess within 10 pounds, you win a prize.
One of these games is a discrete probability distribution and one is a continuous probability distribution. Which is which?

discrete probability distribution
For game 1, you could roll a 1,2,3,4,5, or 6. All of the die rolls have an equal chance of being rolled (one out of six, or 1/6). This gives you a discrete probability distribution of:

Roll 1 2 3 4 5 6
Odds 1/6 1/6 1/6 1/6 1/6 1/6

Albert Harris | Wikimedia Commons

Albert Harris | Wikimedia Commons

For the guess the weight game, you could guess that the mean weighs 150 lbs. Or 210 pounds. Or 185.5 pounds. Or any fraction of a pound (172.566 pounds). Even if you stick to, say, betwen 150 and 200 pounds, the possibilities are endless:

  • 160.1 lbs.
  • 160.11 lbs.
  • 160.111 lbs.
  • 160.1111 lbs.
  • 160.111111 lbs.

In reality, you probably wouldn’t guess 160.111111 lbs…that seems a little ridiculous. But it doesn’t change the fact that you could (if you wanted to), so that’s why it’s a continuous probability distribution.

The following are examples of discrete probability distributions commonly used in statistics:

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