Karteikarten
Poisson Distribution
Karten in diesem Stapel (11)
- 1Poisson Distribution can be written as:X ~ Po(λ)
- 2What does λ represent?The average rate that an vent can occur
- 3Poisson distribution occurs in....A given interval
- 4What are the 4 conditions of Poisson distribution?1. Only whole number of outcomes in given interval
2. Outcomes occur at constant average rate
3. Outcomes occur independently and at random
4. Outcomes occur singly - 5What is the Poisson distribution formula?P(X=x) = e^-λ ((λ^x)/x!)
Where x is number of events occurring in a given time - 6What is 0! ?1
- 7The mean and variance for Poisson distribution are....Both equal to λ
(therefore s.d = root(λ) )
Also mean = s.d^2 - 8The number of bubbles that can occur in a glass of lemonade is at a rate of 4 per cm^3 1. Find probability that 6 bubbles occur in a randomly chosen cm^3 2. Find the probability at least 3 bubbles occur in random cm^3 3. Find the probability that 30 bubbles occur in a randomly chosen 2x2x2 cube off lemonade1. Use calculator or formula for P(X=6) = 0.1
2. P(X≥3) = 1-P(X≤2) , use calculator for 0.76
3. Per cm^3 = 1cm^3 (1x1x1) and 2x2x2 = 8cm^3 , therefore λ is 8 times larger (as 8/1 = 8) , so (4 per cm^3) x 8 = 32 per cm^3 , so λ = 32. We can now use the calculator or the formula for 0.068 - 9The sum of independent Poisson distributions is also.....A Poisson distribution
- 10If X~Po(λx) and Y~Po(λy) , we can say X+Y ~ Po.....X+Y ~ Po(λx + λy)
- 11If X~Po(λx) , we can say that X+X+.....+X ~ Po ....X+X+.....+X ~ Po(λx + λx + .... + λx)
Or if n X terms, then nX~Po(nλx)