Question 3 Let X represent the error in making a measurement of a physical character istic or pr0pert),r (e.g., the boiling point of a particular liquid). It is often reasonable to assume that E(X) = 0 and that X has a normal distribution. Thus the pdf of any particular measurement error is 1 2 189 = 63: /29 f( ) 2W6 where we use 9 i place of 02. Now suppose n independent measures are made, resulting in measurement errors X1 = 1:1, X2 = x2, ..., Xn 2 mn. Obtain the mle of 6. a) Determine the sampling distribution of X = (X1 +X2) /2, calculate EOE ), and compare to E (X1). b) Determine the sampling distribution of the sample variance 32, calculate 13(82), and compare to Var (X1)