8.2 The Geometric Distribution

1
8.2 The Geometric Distribution
2
8.2 The Geometric Distribution

• Definition The Geometric Setting
• A situation is said to be a GEOMETRIC SETTING,
  if the following four conditions are met
• Each observation is one of TWO possibilities -
  either a success or failure.
• All observations are INDEPENDENT.
• The probability of success (p), is the SAME for
  each observation.
• The variable of interest is the number of trials
  required to obtain the FIRST success.

3
8.2 The Geometric Distribution

• Example 8.15 ROLL A DIE
• Example 8.16 DRAW AN ACE

4
8.2 The Geometric Distribution

• A Rule for Calculating Geometric Probabilities
• If X has a Geometric Distribution with
  probability p of success and (1-p) of failure on
  each observation, the possible values of X are 1,
  2, 3, . If n is any one of these values, the
  probability that the first success occurs on the
  nth trial is
• Example 8.17 ROLL A DIE part 2

5
8.2 The Geometric Distribution

• The Geometric Expected Value, Variance and
  Standard Deviation
• Example 8.18 ARCADE GAME

6
8.2 The Geometric Distribution

• Special Formula The probability of waiting more
  than n observations for a first success.

7
8.2 The Geometric Distribution

• Example 8.20 SHOW ME THE MONEY
• 1 01, 02, 03, 04, 05
• Empty 00, 06 through 99
• 23 33 06 43 59 40 08 61 69 25
• 85 11 73 60 71 15 68 91 42 27
• 06 56 51 43 74 13 35 24 93 67
• 81 98 28 72 09 36 75 95 89 84
• 68 28 82 29 13 18 63 84 43 03
• Each student simulate a set until you have a
  success.
• Lets calculate the expected value and standard
  deviation.