Probability - Applications of integrals

In this final application of integrals that we'll be looking at we are going to look at probability.  Previous to actually getting into the applications we require to get a couple of definitions out of the way. 

Assume that we wish to look at the age of a person, height of a person, amount of time spent waiting in line, or maybe the lifetime of a battery.  Every quantity have values that will range over an interval of integers.  Due to this these are termed as continuous random variables.  Continuous random variables are frequently presented by X.

 Each continuous random variable, X, has a probability density function, f(x).Probability density functions that satisfy the following conditions.

1. f (x) > 0 for all x

2. ∫^∞ _-∞  f (x) dx = 1

Probability density functions can be employed to find out the probability that a continuous random variable lies among two values, say a and b. 

This probability is represented by P (a < X < b) and is illustrated by,

P (a < X < b)

=∫^b_a f(x) dx