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# ACMMM136

## 2.1 Discrete Probability Distributions and Mass Functions

#### Discrete Probability Distributions

• The probability distribution for a discrete random variable is a description all the possible values of the random variable, and its corresponding probability.
• Since it is discrete (means there is supposedly/usually a finite number of outcomes), we can express the probability distribution in a table.
• We can describe the probability distribution with the function

p(x)=\operatorname{Pr}(X=x)

where X is the random variable and x is the corresponding values.

• The function above is called a discrete probability function or a probability mass function (pmf).
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## 1.3 Random Variables

#### Random Variable

• A random variable is a function that assigns a number to each outcome in the sample space ε.
• A random variable can be random or discrete.
• A discrete random variable is one that can take only a countable number of values. Note that the numbers does not have any strict pattern (e.g. the numbers can only be whole numbers, rational numbers, the numbers need be an arithmetic or geometric series etc.). Some example would be the number of children in a family, shoe sizes and so on.
• A continuous random variable is one that can take any value in an interval of the real number line. Some examples are height, weight, area and so on.