Probability Distributions Flashcards

1
Q

Under what conditions is the Poisson distribution valid?

A
  • The events must occur randomly
  • The events must be independent of each other
  • The average rate of the events must be constant
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2
Q

What does the geometric distribution model?

A

The random variable: number of trials up to and including the first success

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3
Q

What conditions must hold for the geometric distribution to be valid

A
  • There are trials where all outcomes can be classified into two distinct categories
  • The trials are independent
  • The probability of success, p, is constant for each trial
  • There is no upper limit to the number of trials
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4
Q

For a geometric distribution, what does P(X>x) = ?

A

P(X>x) = (1-p)^x

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5
Q

What are the key phrases in a question which indicate you should use a Poisson distribution?

A
  • Average rate of events
  • Events occuring at a constant rate
  • NEVER a fixed number of trials
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6
Q

What properties of your data indicate the Poisson might be a good model?

A

The mean and the variance are roughly equal (and therefore the standard deviation is the square root of this)

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7
Q

If the number of butterflies seen in 10 minutes is x and you are using a poisson to model the number of butterflies in 1 hour, what is λ?

A

λ = 6x

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8
Q

What can be said about the sum of two independent variables which both follow a Poisson distribution?

A

If two independent variables both follow a Poisson distribution, then so does their sum.

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