Probabilities of a random variable given its cumulative distribution function

The cumulative distribution function gives the probability that a random variable is less than or equal to a particular value x. It can take values from 0 to 1.

F(x) = P(X≤x) = 0 means that the all values of the variable X are greater than x

0< F(x)<1 means that the x is between the extreme values of the variable X or that x lies in between the range of the variable X

F(x)=1 means that x is greater than or equal to the greatest value the variable X can take

For example, the possible returns of a fixed income security in ascending order are given below (in percentages):

-12.50, -10.25, -9.45, -8.20, -4.50, -2.20, 0.05, 1.20, 1.60, 3.35, 5.85, 8.80, 9.90, 10.30, 12.30, 14.10, 15.00

The range of the outcomes is from -12.50 percent to 15.00 percent. So, we can say that:

F(-13.00) = 0
0 F(15.00) or F(20.00)=1

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