Lesson 5.1 Continuous Probability Distribution Functions

Continuous Probability Distribution Function

A continuous probability function f(X) is a special mathematical function used in calculating probabilities. The function f(X) is always greater than or equal to zero and the area between (X) and the x-axis is equal to a probability.

X

The largest probability is 1 and the smallest probability is 0. The area between f(X) and the horizontal x-axis is no larger than 1 and no smaller than 0.

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Continuous Random Variable

A continuous random variable X takes on values that are measured. Individual values of X cannot be listed, just intervals.

Examples:

• Let X = the amount of time a customer stands in line for the ATM machine.
• Let X = a baseball major league batting average.
• Let X = the age of a high school senior the day he or she graduates.
• Let X = the cost of maintenance of a new car during its first year.

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Comparison of Discrete and Continuous Random Variables

A discrete random variable represents outcomes that you COUNT.

A continuous random variable represents outcomes that you MEASURE.

In a discrete graph, the height of a bar is equal to probability.

 

In a continuous graph, probability is equal to the area under the function f(X) and above the x-axis.

 P(X < x) = area to the left of x where x is on the horizontal axis in an x-y graph. 

P(X > x) = area to the right of x.

P(a < X < b) = the area between a and b which are on the horizontal axis.

Because probability = area, P(X =one x-value) = 0.

X

Recall that X =x-value is a vertical line and has no area.

Please continue to the next section of this lesson.

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Up » 5.1 Continuous Probability » 5.2 Uniform Probability » 5.3 Exponentrial Probability