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Math Help - Likelihood and log-likelihood functions

  1. #1
    Senior Member chella182's Avatar
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    Likelihood and log-likelihood functions

    How do you sketch them? I'm utter rubbish at it. I have...

    L(\theta|\mathbf{x})=(2\pi)^{\frac{-n}{2}}exp\{-\frac{1}{2}[\sum_{i=1}^{n}(x_{i}-\theta)^{2}]\}

    ...and...

    l(\theta|\mathbf{x})=-\frac{n}{2}\ln{(2\pi)}-\frac{1}{2}(\sum_{i=1}^{n}x_{i}^{2}-2\theta\sum_{i=1}^{n}x_{i}+n\theta^{2})

    ...which I think equals...

    K+n\bar{x}\theta-\frac{n\theta^{2}}{2}

    ...where K is a constant ( -\frac{n}{2}\ln{(2\pi)}-\frac{1}{2}\sum_{i=1}^{n}x_{i}^{2}) that doesn't depend on \theta.

    But yeah, I don't know how to sketch them. Are they just like normal graphs? Help much appreciated
    Last edited by chella182; April 29th 2009 at 05:13 PM. Reason: I want to subscribe to the thread so I know when someone's replied
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