Distributions GeometricPoisson

Probability Distribution Review

Geometric A discrete probability distribution of a random variable x that satisfies the following conditions. A discrete probability distribution of a random variable x that satisfies the following conditions. 1.A trial is repeated until a success occurs. 2.The repeated trials are independent of each other. 3.The probability of a success (p) is constant for each trial.

Typical Problem Rolling a 5. Rolling a 5. –Find the probability that the first success will occur on trial number 4. Failure (5/6) Failure (5/6) Success (1/6) Success (1/6)

Geometric Formula x = the number of attempts for a success to occur p = the probability of a success q = the probability of a failure

Another Example LeBron James is a 78% free throw shooter. What’s the probability that if he shoots, his first miss will occur on his 6th shot? LeBron James is a 78% free throw shooter. What’s the probability that if he shoots, his first miss will occur on his 6th shot?

Poisson A discrete probability distribution of a random variable x that satisfies the following conditions. A discrete probability distribution of a random variable x that satisfies the following conditions. 1.The experiment consists of counting the number of times, x, an event occurs in a given interval. The interval can be an interval of time, area, or volume. 2.The probability of the event occurring is constant for each interval. 3.The number of occurrences in one interval is independent of the number of occurrences in other intervals.

Poisson Formula = The average number of occurrences in one interval = The average number of occurrences in one interval x = The number of expected occurrences in an interval

Typical Problem The average number of unintelligent questions in a block by Geometry students is 6. What’s the probability that they ask 5 unintelligent questions next block? The average number of unintelligent questions in a block by Geometry students is 6. What’s the probability that they ask 5 unintelligent questions next block?

Another Example A man on the beach is looking for buried treasure with a metal detector. On average, he finds 4 metal objects per acre. What’s the probability he finds 5 metal objects in the next acre? A man on the beach is looking for buried treasure with a metal detector. On average, he finds 4 metal objects per acre. What’s the probability he finds 5 metal objects in the next acre?