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Poisson Distribution (DP IB Applications & Interpretation (AI))

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    What is the Poisson distribution?

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  • What is the Poisson distribution?

    The Poisson distribution is a discrete probability distribution that counts the number of occurrences in a fixed length of time or space.

  • What are the two conditions necessary in order to use a Poisson distribution?

    The two conditions necessary in order to use a Poisson distribution are:

    1. Occurrences are independent.

    2. Occurences occur at a uniform average rate (m).

  • What notation is used to show that a random variable X has a Poisson distribution?

    The notation used to show that random variable X has a Poisson distribution, is X tilde Po open parentheses m close parentheses

    Where:

    • m is the average rate of occurences

    The symbol 'tilde' means 'is distributed as'.

  • True or False?

    If X follows a Poisson distribution, then its mean and standard deviation are equal.

    True.

    If X follows a Poisson distribution, then its mean and variance are equal.

  • If X follows a Poisson distribution, then what values can X take?

    If X follows a Poisson distribution, then X can take any integer greater than or equal to zero.

  • If X tilde Po invisible function application open parentheses m close parentheses and Y tilde Po invisible function application open parentheses lambda close parentheses are independent then what is the distribution of X plus Y?

    If X tilde Po invisible function application open parentheses m close parentheses and Y tilde Po invisible function application open parentheses lambda close parentheses are independent then X plus Y tilde Po invisible function application open parentheses m plus lambda close parentheses.

  • True or False?

    The parameter for the Poisson distribution, m, can be any positive number.

    True.

    The parameter for the Poisson distribution, m, can be any positive number.

    It can be a decimal or an integer.

  • If X tilde Po open parentheses 4.5 close parentheses is used to model the number of customers in 10 minutes, then which distribution could be used to model the number of customers in 60 minutes?

    If X tilde Po open parentheses 4.5 close parentheses is used to model the number of customers in 10 minutes, then Y tilde Po open parentheses 27 close parentheses could be used to model the number of customers in 60 minutes.

    The parameter is found using proportionality: 10 cross times 6 equals 60 and 4.5 cross times 6 equals 27.

  • What two pieces of information are needed to calculate straight P open parentheses X equals x close parentheses using a calculator's Poisson distribution function?

    To calculate straight P open parentheses X equals x close parentheses using a calculator's Poisson distribution function, you need:

    • the x value,

    • the mean, m.

  • True or False?

    If X tilde Po open parentheses m close parentheses, then straight P open parentheses X less than 4 close parentheses equals straight P open parentheses X less or equal than 3 close parentheses.

    True.

    If X tilde Po open parentheses m close parentheses, then straight P open parentheses X less than 4 close parentheses equals straight P open parentheses X less or equal than 3 close parentheses.

  • If X tilde Po open parentheses m close parentheses, how could you calculate straight P open parentheses X greater or equal than 5 close parentheses?

    If X tilde Po open parentheses m close parentheses, then straight P open parentheses X greater or equal than 5 close parentheses equals 1 minus straight P open parentheses X less or equal than 4 close parentheses.

    You can also use a large number for the upper bound, i.e. straight P open parentheses X greater or equal than 5 close parentheses almost equal to straight P open parentheses 5 less or equal than X less or equal than 999999 close parentheses.

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