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Poisson distribution - Discrete Probabilites

Poisson distribution

Lessons

Notes:
The Poisson Distribution is an approximation to the Binomial Distribution.

Recall:
P(x)=nCxpx(1p)nxP(x)= {_n}C_{x}\;p^x(1-p)^{n-x}
nn: number of trials
xx: number of success in n trials
pp: probability of success in each trial
P(x)P(x): probability of getting x successes (out of n trials)
μ=np\mu=np
Now:
μ=λ=np\mu=\lambda=np

Poisson Distribution:
P(x)=eλP(x)=e^{-\lambda} λxx!\frac{\lambda^x}{x!}
• poissonpdf (λ,x)(\lambda,x)
• poissoncdf (λ,x)(\lambda,x)
  • 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;
    • c)
      Compare your previous two answers
  • 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,
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Poisson distribution

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