What is a discrete probability distribution and how is it different from a continuous probability distribution
A discrete probability distribution is often defined as a probability distribution in which the outcome of each event or event set can be determined by a unique value. In other words, a discrete probability distribution is composed of unique events that each have assigned probabilities. Discrete distributions are commonly seen in many everyday contexts such as the outcomes of dice rolls and outcomes of coin flips but they can also be found with examples such as male and female births or people who earn six figures annually. A continuous probability distribution is widely recognized as a probability distribution in which each outcome of an event or event set can, theoretically, take on any number within a range. For example, the outcomes of the earned income category are all real numbers and not composed of unique events. Continuous distributions are widely seen in many everyday contexts such as measurements on scales such as weight, height and time.
continuous probability distribution example: http://www.google.com/search?hl=en&q=%22graphs+of+statistics&btnG=Google+Search
Slightly more advanced example: http://stats.idre.ucla.edu/satsc/satsc_chap18.pdf
Examples of discrete probability distributions
There are several discrete probability distributions that are commonly seen and used as examples in statistics and probability. They include: – Binomial distribution
– Poisson distribution
– Gaussian distribution
– Beta distribution
– Geometric distribution
The examples below will illustrate what these distributions are and how they are used in algebra.
p(x) = probability that x number of successes will occur (x > 0)
## “Binomial Distribution” is the only discrete probability distribution that takes a parameter, n, which must be greater than or equal to 0. Consider generating a random number between 0 and 10:
With this knowledge, we can see that the number of random numbers between 0 and 10 that are less than or equal to 3 is:
How to find the mean, median, and mode of a discrete data set
Armed with the information that your data set follows a discrete probability distribution, you can calculate the mean, median and mode of the data set. There are two different ways to find these values but both methods rely on using the sum of all possible outcomes and applying conditional probability to determine these values: 1. If the discrete probability distribution is a finite set of outcomes, the mean and median can be found by multiplying each outcome times its corresponding probability and summing all products. The mean then has to be divided by the sum of all outcomes to determine the arithmetic mean. 2. If the discrete probability distribution is a finite set of outcomes or complete, the mean and median can be found by summing each outcome times its corresponding probability and dividing by the sum of all outcomes to determine the arithmetic mean. The median can be found using a similar procedure using the modulus instead of the sum as it is easier to calculate floating point numbers in this manner.