Cumulative Distribution Functions

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A probability distribution tells you the probability of something happening,the probability of the random variabletaking the valueA Cumulative distribution tells you the probability of the random variabletaking a value less than or equal to a valueoften written

Given a probability distributionwe can find the cumulative distribution:

Ifis presented in a table, add the entries as you go along.

1 2 3 4 5
0.1 0.3 0.15 0.05 0.4
0.1 0.1+0.3=0.4 0.1+0.3+0.15=0.55 0.1+0.3+0.15+0.05=0.6 0.1+0.3+0.15+0.05+0.4=1

Ifis presented as a function, integrate. Supposethen

Given a cumulative distributionwe can find the probability distribution:

Ifis presented in a table, subtract successive entries as you go along.

1 2 3 4 5
0.1 0.4 0.55 0.6 1
0.1 0.4-0.1=0.3 0.55-0.4=0.15 0.6-0.55=0.05 1-0.6=0.4

Ifis presented as a function, differentiate. Supposethen

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