Upcoming SlideShare
×

# Geometric distributions

150

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
150
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
1
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Geometric distributions

1. 1. Geometric Distribution
2. 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. 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
1. #### A particular slide catching your eye?

Clipping is a handy way to collect important slides you want to go back to later.