Question

Two identical radars produce independent unbiased estimates on the range of an incoming car. The standard error of Radar 1 is 3 feet and the standard error of Radar 2 is 6 feet. Radar 1 reports a car coming in at range of 100 feet and Radar 2 reports it at 110 feet. Use a linear combination of the two location estimates on the car to provide the Minimum Variance Unbiased Estimate of the car's range. Also provide the standard error of the estimate.

Answer 1

is loa Now since ♡ Given two identical and independent estimators on range of the incoming car as X,X2 where estimate of X is 110 with s.e. 3 & estimate of x2 with s.e. 2 BLUE is there. the Best linear Unbiased Estimator - 8 Minimum Variance Unbiased estimator CMUVE) Let MUUEn be a linear combination of X, 8x2 w where 2=0X, +(1-x) X2 whered is to be selected such that 2 is MVOE. (2, say) ماهه Since x, & Xz are unbiased estmator 2 is also an unbrand estimator. SOME & Honce AMSE(2) = Var (2) = x² Var(x,) + (1-x)² Var (x2) + 2 &(1-x) con CY, ,X2) [cov (KG «X2)=0 - eb 9x²4 4 (1-x)² are independent Miningizing M wort a weget 9 180 - 8(1-2) = 0 since X, 8x₂ am 2-0 = 266 : $8 =) X = 4 13 IMI to, hence Mis minimumat da bx=9/13 x = 42 Hence oun Muokis 2 = 4X+9x2 with standard 13 error = 6 113