2. 4 Parts of a Geometric Distribution
1. Outcomes are success or not success
2. Probability of success is fixed
3. Trials are Independent
4. No fixed number of trials – try until you succeed
Examples:
Probability of your first foul shot success being on your tenth try
Probability of having 5 boys and then a girl
Mean of Geometric Distribution: (not given on formula sheet)
1
E(X) = 𝜇 =
𝑝
Standard Deviation of Geometric Distribution: (not given on
formula sheet)
𝜎=
1−𝑝
𝑝
3. Examples of Geometric Distribution:
What is the probability that you will have five boys and then a girl?
Trial # 1
2
3
4
Prob
0.5
0.5*0.5 0.52 ∗ 0.5
0.5
0.55 ∗ (0.5)
5
0.53 ∗ 0.5
6
0.54 ∗
Notice that each trial is calculated by:
probability of failing before * probability of success
So P(5boys then girl ) = 0.55 ∗ (0.5) = 1.5625 x 10−8
What is the probability that you will have at most 3 children before you
have a girl?
P(g) + P(b,g) + P(2b,g) = 0.5 + 0.5*0.5 + 0.52 ∗ 0.5 = 0.875
How many children can you expect before you will have a girl?
1
1
E(X) = =
=2
𝑝
0.5
You can use your calculator : Geometric Pdf and Geometric Cdf
