Geometric Distribution
4 Parts of a Geometric Distribution
1. Outcomes are success or not success
2. Probability of success is fixed
3. Trials ar...
Examples of Geometric Distribution:
What is the probability that you will have five boys and then a girl?
Trial # 1
2
3
4
...
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Geometric distributions

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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
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