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Probability Distribution Table – Definition & Examples

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A probability distribution table is a table that shows the probabilities of occurrence of an event in tabular form corresponding to the value of the random variable.

Example:

Suppose that a die is thrown. Let X denote the number that occurs on the uppermost face of the dice. Then X is a random variable since we cannot predict what number will occur on the die in advance. Each of the numbers 1,2,3,4,5 and 6 has a one out of six chance of occurring. The probability distribution table looks like,

Random Variable XProbability P(X)
11/6
21/6
31/6
41/6
51/6
61/6

Notice that the sum of all the probabilities in our table adds up to 1. This is true in general and in fact, this property can be used to complete a probability distribution table.

How to complete a probability distribution table?

In order to find the missing value in a probability distribution table, we make use of the fact that the sum of all the probabilities should add up to 1. Consider the following incomplete distribution table,

Random Variable XProbability P(X)
10.1
2?
30.2
40.3

Let the unknown probability value be a. We have that,

P(X=1) + P(X=2) + P(X=3) + P(X=4) = 1 0.1 + a + 0.2 + 0.3 = 1 \implies 0.6 + a = 1 \implies a = 0.4

So the completed probability table looks like,

Random Variable XProbability P(X)
10.1
20.4
30.2
40.3

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