I want the pmf to be able to calculate the expected value.

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Hi Da Vinci

A probability mass function is a function that maps from the (discrete) sample space to the real interval \([0,1]\).

Assuming that the sample space of the random variable \(X\) is finite this means that all possible values can be listed in some way. Therefore, in order to find the pmf you need to specify the relative frequency of each outcome from the sample space.

For example, suppose \(X\) is the outcome when a fair dice is rolled. The sample space of \(X\) is the set \(\{1,2,...,5,6\}\).

From this can you find the pmf of \(X\)?

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