Transcript 7.3 Geometric Distribution

GEOMETRIC DISTRIBUTION
Geometric Distribution
In some situations, the critical quantity is the WAITING
TIME (Waiting period)
 number of trials before a specific outcome (success)
occurs
 has only two outcomes, success or failure
 the difference is the waiting time, the number of failure
trials before success occurs.
Apply the product rule to find the probability of
successive independent events. Each unsuccessful event
adds another factor to the probability, making it look like
P(x) = qxp, where p and q are the same as we know them.
Expectations for a Geometric Distribution
q
xP
(
x
)

E(x) =
= p but this expectation converges to a
simple formula.

x 0
If we are looking for the amount of time before a failure
occurs, a success is actually failing something, which
means that p becomes q, and q becomes p.
Ex. Suppose that an intersection you pass on the way to
school has a traffic light that is green for 40s and then
amber or red for a total of 60s.
What is the probability that the light will be green when
you reach the intersection at least once a week?
Remember: there are 5 days in a school week, therefore
we need to look at P(0 < x < 4)
Why did we add?
Homework
Pg 394 # 1,3,6,7