Transcript Geometric Distribution & Poisson Distribution

Geometric Distribution
&
Poisson Distribution
Week # 8
Geometric Distribution:
• A trial is repeated until a success occurs.
• The repeated trials are independent of each
other.
• The probability, p, is constant for each trial
Formula:
x 1
P( x)  p(q) , where: q  1  p
When it is used:
Ex (1) – Prizes are being awarded in a raffle.
The tickets get put back into the hat each
time there is a drawing. Your name is
placed in a hat with nine others. Find the
probability that your name will be pulled
on the 5th draw?
51
P(5)  (1/10)(9 /10)
P( x)  .06561
So what happened in Ex (1)
• We were looking for a specific time for our
event to happen: Trial # 5
• So, we wanted 1 success and 4 failures
51
P(5)  (1/10)(9 /10)
Use on the TI-83
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2nd DISTR
Scroll down to Geometpdf(
Put in the P(E),number of trials
Geometpdf(prob,# of trials)
Hit enter!
Tom Brady
Tom Brady completes 65% of his pass
attempts. Find the following:
(a)What is the probability he will complete a
pass on his 5th throw?
(b)What is the probability of him finally
completing a pass on his 10th throw?
Let’s try one more…..
– Coin toss.
a: P(heads) on the first toss?
b: P(heads two times in a row)?
c: P(the first heads that happens is on the
third toss)?
d: P(heads will occur on the 5th or 6th toss)?
e: P(the first heads occurs on the 37th toss)?
Poisson Distribution:
• Counts the number of times an event
occurs in a given interval, you must know
or be given the MEAN (μ).
• The Probability is the same for each event.
• The number of occurrences in one interval
is INdependent of the number of
occurrences in another window.
x 
Formula:
 e
P( x) 
x!
Let’s try one….
Ex (3) – The average number of days of sun
in the month of December in Buffalo is 12
days. What is the probability that next
December there will be 15 days?
P( x) 
 e
x

x!
15 12
12 e
P( x) 
15!
P( x)  .0724
Extending:
• Let’s do PRB # 22 from p. 227……
A newspaper finds that the mean number of
typographical errors per page is 4.
(a)Find the probability that there are going to
be 3?
(b)Find the probability that there are going to
be 7?
Using the TI-83
2nd DISTR
Scroll down to Poissonpdf(
Type in the mean(μ), x value.
Poissonpdf(12,15) for the last problem.
You must be able to…..
• determine when to use:
– Binomial Distribution
– Geometric Distribution
– Poisson Distribution
• See page 225…..