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Math Help - Gamma random variable problem

  1. #1
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    Gamma random variable problem

    Question: Let X be a gamma random variable with \mu = 21 and \sigma^2 = 63. Find P(18 \leqX \leq30).

    I have calculated that \beta=3 and \alpha=7

    but I'm not sure how to turn the interval 18 to 30 into some interval I can find in the tables.

    Can you help?
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  2. #2
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    Re: Gamma random variable problem

    You say "the tables" as if we are looking at them too, or all tables have the same contents.


    if i was using my tables (Tables and formulae for UK actuarial exams) i would use the following relationship:

    \text{if } X \sim \chi ^2 (v) \text{ then } cX \sim \Gamma(0.5v,2c)

    This can be used to re-express your gamma probability as a chi-square probability. Chi-square distributions are tabulated.

    If this isn't familiar, I assume your professor showed you one before giving you the question? how did he do it?
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  3. #3
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    Re: Gamma random variable problem

    Sorry. All I have been given is an Incomplete Gamma Function Table where 1<=y<=15 and 1<=alpha<=10. Can I subtract 30-18 and use the value of 12 on this table? or am I way off.
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