Question-246 points) Suppose You have a population following a Normal distribution with population 183.11 p and population variance 52. Assume n is unknown and you are interested in estimating it. You ecide to draw 5 sample values [X1,X2, ..., X5]. You haven't observed them yet, so for now we treat them as iriables. Someone proposes these following two estimators for p, 1 T1 = 5(X1 +X2 + +X5] nd T2 = 0.1X1 + 0.2X2 + 0.4.X3 + 0.2X4 + 0.1X5 ) [1.5 points] Using separate calculations, check whether T1 and T2 are unbiased estimator of p. or not? If ot, calculate the Bias. ) [1.5 points] By calculating the variance for each of these estinlators calculate their corresponding Mean quared Errors (MSE). ) [1.5 point] Determine the sampling distribution of T1 and T2. Conm'ient on what distribution they will ow (why) along with corresponding parameters. .) [1.5 point] If you were to calculate two separate 95% condence intervals (CI) for it, one based on T1 nd the other based on T 2, which CI would be wider and why? [no calculation needed] ihow detailed calculation in parts (a) and (b]]