Transcript Data Management

Geometric
Distribution

Similar to Binomial
• Success/Failure
• Probabilities do NOT change


Now you are looking at the number
of failures until a success.
Determining the prob2€
ity that you
will have to wait for a certain amount
of time before an event occurs
Probability and Expectation for
Geometric Distribution
q
E ( x) 
p
P( x)  q p
x

Where p is the
probability of a
success in each
single trial and q is
the probability of a
failure

The expectation
converges to a
simple formula
Ex
Jamaal has a success rate of 68% for
scoring on free throws in basketball.
What is the expected waiting time
before he misses the basket on a
free throw?
The random variable is the number of trials before
he misses a free throw
A success is Jamaal failing to score
q=0.68
p=1-0.68=0.32
q
E( X ) 
p
0.68

0.32
 2.1
Ex
Suppose that an intersection you pass on
your way to school has a traffic light
that is green 40 s and then amber or
red for a total of 60s
a) What is the probability that the light
will be green when you reach the
intersection at least once a week?
b) What is the expected number of days
before the light is green when you
reach the intersection?
a) What is the probability that the light will be green
when you reach the intersection at least once
a week?
p= light is green = 40/100 = 0.40
q= light not green = 60/100 = 0.60
There are 5 school days so we want
the probability that you will wait 0
days, 1 day , 2 days, 3 days or 4
days before it is green
P(0,1, 2,3or 4)
 0.40  (0.6)(0.4)  (0.6) (0.4)  (0.6) (0.4)
2
(0.6) (0.4)
4
 0.92
3
b) What is the expected number of days before the light is
green when you reach the intersection?
q
E( X ) 
p
0.6

0.4
 1.5
The expected
waiting time
before catching a
green light is 1.5
days
Homework!
Pg 394
#1,2,3,7,9,10