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Thread: Need a formula for a one of these gamma densities

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    Need a formula for a one of these gamma densities




    For the integral from [0, infinity] for x^(s-1) * e^(-lambda * x)

    You have s and lambda, so is the final answer for this (s-1)! / lambda^(s) ? Or is it (s-1)! / lambda ^(s-1) ?

    I understand this, but the only question I have is in the denominator.

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    Re: Need a formula for a one of these gamma densities

    Are you assuming s is an integer? Otherwise you should probably use the gamma function. Anywho, can you think of anyway to check which of those answers is correct? Possibly using the fact that a gamma density integrates to 1?

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    Re: Need a formula for a one of these gamma densities

    Quote Originally Posted by Dason View Post
    Are you assuming s is an integer? Otherwise you should probably use the gamma function. Anywho, can you think of anyway to check which of those answers is correct? Possibly using the fact that a gamma density integrates to 1?
    Yes, s is the integer, and this gamma density integrates to 1.

    My question is for the lambda part in the denominator, is it lambda^(s) or lambda^(s-1) ?

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    Re: Need a formula for a one of these gamma densities

    The main part of the post is saying you should be able to deduce which it is by using the fact that a gamma density integrates to 1. Which of the two do you think it is and why?

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    Re: Need a formula for a one of these gamma densities

    Quote Originally Posted by Dason View Post
    The main part of the post is saying you should be able to deduce which it is by using the fact that a gamma density integrates to 1. Which of the two do you think it is and why?
    It's the one with lambda ^ s, just remembered the entire gamma density formula, wrote it out, and this one is the one for the gamma density to integrate to one.

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    Re: Need a formula for a one of these gamma densities


    There you go. Good job.

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