Likelihood and log-likelihood functions

**chella182** · April 29th 2009, 02:44 PM

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

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