Hi all Several queries on CT6 1. In CT6-03 at the end of page 14, how does the skew tell us whether the median will be greater than or less than the mean? 2. In CT6-03 at the top of page 19, what is meant by the statement that the MLE of a function equals the function of the MLE? 3. In CT6-07 page 7 at the end of the second paragraph, it says that it is a mixed distribution because of the possibility that N = 0. Why is the=is needed? Surely it would be a mixed distribution even if N could not be 0! Many thanks
1. For Symmetric distribution Mean=Mode=Median For Positively skewed distribution Mean>Median>Mode For Negatively skewed distribution Mode>Median>Mean 2. It means if MLE of \(\theta\) is \(\hat\theta\) then MLE of \(f(\theta)\) is \(f(\hat\theta)\) 3. Mixed distribution is a distribution which is continuous in some range and is also discrete at some points. Here because of the possibility of N=0 there will be a probability mass at S=0 and if value of N is more than 0 then S becomes continuous because here they are considering continuous X.
