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Thread: Finding the expectation of X_2

  1. #1
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    Finding the expectation of X_2

    Given $\displaystyle (X_1,X_2,...,X_{k-1})$ has a Dirichlet distribution wiht parameters $\displaystyle (\alpha_1,...,\alpha_k)$

    With $\displaystyle \alpha_{i+}=\alpha_i+...+\alpha_k$

    I want to find $\displaystyle E[X_2]$

    I know that $\displaystyle E[X_1]=\frac{\alpha_1}{\alpha_{1+}}$ since $\displaystyle X_1 \sim Beta(\alpha,\alpha_{2+})$

    and

    $\displaystyle (\frac{X_2}{1-X_1}|X_1) \sim Beta(\alpha_2,\alpha_{3+})$
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Finding the expectation of X_2

    If you want to use latex you have to use [ tex ] ... [ /tex ] in stead of [ math ] ... [ /math ]
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  3. #3
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    Re: Finding the expectation of X_2

    Thank you for your correction
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