Discrete Probability Distributions

Discrete Probability Distributions

1. Binomial Distribution

   • Example
     • Historical sales record that 40 percent of all customers who enter store make a purchase. What is the probability that two of the next three customers will make a purchase?
     • how we know it's binomial
       • 1) identical trials
       • 2) TWO outcomes are possible in each trial
       • 3) probability stays constant
       • 4) all trial outcomes are independent
     • Sample Outcome Space
       • SSS    SSF SFS FSS FFS FSF SFF FFF
       • We know there are 8
     • Note
       • 1
         • the 3 in this expression is the number of sample space out comes (ssf, sfs, and fss) that correspond to the EVENT "two of the next three customers make purchases.
       • 2
         • .4 = p .6= q  is the probability that the customer does not make a purchase
     • Calculation

2. Definitions

   • trials
   • success and failure
     • (p)= success (f) = failure
   • sample space outcomes

3. Formulas

   • number of ways to arrange x successes among n trials
   • Binomial Probability

4. Rules

   • Addition Rule
     • not mutually Exclusive
     • Mutually Exclusive
   • Compliment Rule
     • If A is the event... A Compliment is the event in which it will NOT occur.

5. Mean/ Variance/ SD

Images and files in the map