# Likelihood of a given sample [closed]

Hi, i am fairly new on these forums, so please let me know, if information or formulation is lacking.

My question is related to the picture i have linked. My problem is i really don't understand how the likelihoods of $\theta$ is derived and my intuition of likelihood functions is lacking a lot. Could anyone explain to me how i would go on about solving these problems? I find (c), (d), (e) especially hard to grasp.

Thanks a lot :)

• hey @Chris, check this out and maybe consider adding the 'self-study' tag stats.stackexchange.com/tags/self-study/info Sep 8, 2017 at 16:54
• Do you any definition of likelihood? Can you give your solutions for (a) and (b)? Sep 8, 2017 at 18:02
• I know the definition of likelihood, my solution for (a) is the product of all the normal density functions of each attribute with a mean of $\theta$ and the SD of the given sample. (b) is then the same solution but with the standard deviation given as $\frac{SD(x)}{\sqrt{n}}$, since we only got the sample mean. I am getting a bit lost at (c), (d) and (e). Sep 8, 2017 at 18:19
• NB The q. does say "$\sigma^2$ is known at the observed sample variance". Please edit your question to show your working & where you're stuck. Sep 9, 2017 at 19:29