Stats - Distributions

(1) For sample a: of size n distributed as N (a, or) the sum of squared errors (SSE) of mean estimate ,u is given by 1']. SSEOU) = 2m a\")? i=1 (a). Demonstrate using differentiation that the SSE point estimate it, corresponding to the value of ,u that minimises the SSE, is equivalent to the sample mean (b). An alternative measure of goodness-oft to estimate the mean :1. and standard deviation or is maximum likelihood estimation where for sample 1: = (3:1, . . . ,ctn) the likelihood for the normal distribution, N (a, a), is ptxlm) = (%)iexp(%os)2). i=1 Why does this expression involve the product of functions of mi? Why is the likelihood a measure of goodness-of-t to estimate the mean it and standard deviation 0