Geometric Distributions
p. 544 42,44
p. 550 46,48,50

Let X = number of rolls until a 3 occurs

Write out the probability distribution for X
X
P(x)

Prove the this is a valid probability
distribution by showing Σp(x) = 1.
Histogram for G~(1/6)

an = a1* r

Sn = a1 (1 – rn)/ (1 –r)

S = a1/(1-r)
(n-1)
(if -1≤r≤1)

For the geometric sequence
100,50,25,12.5,…..

Find the formula for an

Use formula to calculate a8

Find S5

Find S
X
1
2
3
P(x)
S = Σp(x) =
4
5
6
7 8
9
10
......
 µx
=
 Multiple
 Now
by sides by q :
subtract the two equations:

P(X
n) = 1 – p(X ≤ n) =
1 – (p + qp+q2p + …..+ qn-1 p) =
1 – p( 1 + q + q2 + …..+ qn-1) =
1 – p ( 1 – qn/ (1 – q))
1 – (1 – qn) =
qn

Roll a die until a 3 is observed . Find the
probability that it takes more than 6 rolls .



Glenn likes the game at the state fair where you
toss a coin into a saucer. You win if the coin
comes to rest in the saucer without sliding off.
Glenn has played this game many times and has
determined that on average he wins 1 out of 12
times he plays. He believes that his chances of
winning are the same for each toss and he has no
reason to think his tosses are not independent.
Let X be the number of tosses until a win. Glenn
believes that this describes a geometric setting.
What is µx?
What is σx?