# Thread: Likelihood and log-likelihood functions

1. ## 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