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Math Help - Application of Chebshev's Inequality

  1. #1
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    Application of Chebshev's Inequality

    Hi!

    I have the following problem:

    Suppose X ~ Poisson (Lambda). Show P(X > 2lambda) =< 1/lambda

    So I wrote out Chebshev's by definition:

    P(|X - u| > t) =< V(x)/t^2

    I made a simple substitution of t = lamda and proceeded.


    P(|X-lamda| > lamda) = P(X > 2lambda) = lambda/lambda^2 =< 1/lambda


    Does this make sense?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jamesmartinn View Post
    Hi!

    I have the following problem:

    Suppose X ~ Poisson (Lambda). Show P(X > 2lambda) =< 1/lambda

    So I wrote out Chebshev's by definition:

    P(|X - u| > t) =< V(x)/t^2

    I made a simple substitution of t = lamda and proceeded.


    P(|X-lamda| > lamda) = P(X > 2lambda) = lambda/lambda^2 =< 1/lambda


    Does this make sense?
    Yes

    CB
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