1. T HE G EOMETRIC AND P OISSON D ISTRIBUTIONS

2. G EOMETRIC D ISTRIBUTION – A GEOMETRIC DISTRIBUTION SHOWS THE NUMBER OF TRIALS NEEDED UNTIL A SUCCESS IS ACHIEVED. Example: When shooting baskets, what is the probability that the first time you make the basket will be the fourth time you shoot the ball?

3. C ONDITIONS FOR G EOMETRIC D ISTRIBUTION 1. A trial is repeated until a success occurs 2.The repeated trials are independent for each trial 3. The probability of success p is constant 4.The random variable x represents the number of the trial in which the first success occurs

4. G EOMETRIC D ISTRIBUTION E QUATION P ( x ) = p ( q ) x – 1 p = the probability of success q = 1 – p x is the random variable(what you are looking for!)

5. C ONNECTION TO G EOMETRIC S ERIES

6. E XAMPLE

7. P OISSON D ISTRIBUTION – U SE WHEN YOU ARE LOOKING FOR THE NUMBER OF TIMES SOMETHING OCCURS DURING A GIVEN INTERVAL. Example: How many accidents will occur at the intersection of Chandler Blvd and Arizona Ave between 11:30 p.m. – 12:30 p.m.

8. P OISSON D ISTRIBUTION The experiment counts how many times, x, an event occurs in a given interval. The probability of the event occurs is the same for each interval The number of occurrences in one interval is independent of the number of occurrences in other intervals.

9. P OISSON E QUATION

10. E XAMPLE FOR P OISSON D ISTRIBUTION

11. Complete the 4.3 Classwork