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Poisson distribution
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Poisson distribution
Lessons
The Poisson Distribution is an approximation to the Binomial Distribution.
Recall:
• P(x)=nCxpx(1−p)n−x
n: number of trials
x: number of success in n trials
p: probability of success in each trial
P(x): probability of getting x successes (out of n trials)
• μ=np
Now:
• μ=λ=np
Poisson Distribution: P(x)=e−λx!λx
• poissonpdf (λ,x)
• poissoncdf (λ,x)
Recall:
• P(x)=nCxpx(1−p)n−x
n: number of trials
x: number of success in n trials
p: probability of success in each trial
P(x): probability of getting x successes (out of n trials)
• μ=np
Now:
• μ=λ=np
Poisson Distribution: P(x)=e−λx!λx
• poissonpdf (λ,x)
• poissoncdf (λ,x)
- IntroductionWhat is the Poisson Distribution?
- 1.Determining the Poisson Distribution
The number of meteors that hit the earth in a given day is modelled by a Poisson Distribution with λ=4. What is the probability that 5 meteors hit the earth in a day? - 2.When making a video I typically make 1 error for every 20 minutes of video time. If I make 45 minutes of video what is the probability that I make 3 errors?
- 3.In a particular community the average person survives to age 100 with probability 0.005 (which is equivalent to 0.5%). If this community has 2,000 people, then what is the probability that 15 people in this community survive to age 100 using;a)The Binomial Distributionb)The Poisson Distributionc)Compare your previous two answers
- 4.Cumulative Poisson Distribution
On U.S. route 66 (an American highway) every car that travels this whole route has a probability of p=0.0002 of getting into a car accident. A total of 10,000 cars drive this route every month. What is the probability that there are fewer than 3 car accidents in a month? - 5.Determining the Poisson Distribution using Calculator Commands
A fair coin is flipped 10 times, what is the probability using the Poisson Distribution commands on your calculator find,a)The probability that heads comes up 5 times?b)The probability that heads comes up 5 or less times?c)The probability that heads come up more than 7 times?
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4.
Discrete Probabilities
4.1
Probability distribution - histogram, mean, variance & standard deviation
4.2
Binomial distribution
4.3
Mean and standard deviation of binomial distribution
4.4
Poisson distribution
4.5
Geometric distribution
4.6
Negative binomial distribution
4.7
Hypergeometric distribution
4.8
Properties of expectation