Distributions with dependent trials whose outcomes are either success or failure We dont talk about p and q, because the probabilities change
Items are removed from the set, you use the hypergeometric distribution
Formula
The probability of outcomes x successful outcomes in r trials is: r : # of selections a : what random variable x will take from. the success set. number of possible successes n : population total set(universal set fit within the selection space)
Memorizing the formula
Expectations
Example
Probability distribution of the number of hearts in a 5 card hand from a standard deck of cards
| Number of hearts, x | P(x) | x P(x) |
|---|---|---|
| 0 | () = 0.2215 | 0 |
| 1 | () = 0.4114 | 0.4114 |
| 2 | () = 0.2743 | 0.5486 |
| 3 | = 0.815 | 0.2445 |
| 4 | = 0.0143 | 0.0572 |
| 5 | = 0.0005 | 0.0025 |
| The expected value is the sum of column x P(x). that is 1.26 | ||
| What this means is that we are expected to get 1.26 hearts for every 5 card hand |
Example 2. Find population
in 2002, 300 tagged bass released. in 2003, 200 bass caught and 20 found were tagged. what is the estimate size of bass population in 2003?
n = ? a = 300 r = 200
E(x) = ra/n n = ra n = 3000