Question : Claim amounts of a certain type are modelled using a normal distribution with an unknown mean and a known standard deviation £20. For a random sample of 20 claim amounts all that is known is that 5 of them are greater than £200. (i) let theta be the probability that a claim amount is greater than £200. Find MLE of theta. (ii) determine theta in terms of 'm' and hence calculate MLE of 'mu'. My query: In part (i) for i=1 to 15, the likelihood function is not having any theta. For 16 to 20 only it is theta^5. (see attached pic). How to proceed then? In part (ii) does 'm' mean sample mean? How is it connected to theta then? Kindly help.
i) If 5 are greater than £200 then 15 are less than £200 ii) I have no idea what m is - it hasn't been defined in the question - I would suspect they meant mu but there was a typo. In which case use the invariance property of estimators to transform your theta = P(X>200) into something with mu in.
