Question

In many problems we interested in estimation of the population mean. Let X1; : : : ;X10
be a random sample from a population with mean and variance 2. Consider the
following estimators for estimating :
^
1 =
X1 + X2 + + X10
10
; ^
2 =
3X1 ? 2X5 + 3X10
2
:
Compute the variance of the estimators.
A. V[^
1] = 2=10, V[^
2] = 112=2 B. V[^
1] = 32=2, V[^
2] = 32=7
C. V[^
1] = 2=10, V[^
2] = 82=2 D. V[^
1] = 2=100, V[^
2] = 42=2
E. none of the preceding

In many problems we interested in estimation of the population mean. Let X1, ..., X10 be a random sample from a population with mean y and variance o?. Consider the following estimators for estimating : X1 + X2 + Ô1 3X1 – 2X5 + 3X10 10 2 Compute the variance of the estimators. + X 10 1 = = A. V[01] = 02/10, V[@2] = 1102/2 B. V[@1] = 302/2, V[Ô2] = 302/7 C. VÔ1] = 02/10, V[O2) = 802/2 D. V[Ô1] = 02/100, V[@2] = 402/2 E. none of the preceding

Answer 1

Question - E(X)= u ; i = 1,2,---,10 2 Var (xi)=02 +X10 vas ( )= Vas (x1+x2+ wel . (x,-)] 10 hoof var (x) + Vor(xx)+ tor loo [100?] [ 0²+0² - + JO 2 Thus, = Var (@) Var (62) = vas (3 x7–2X5+3 X10 ) = +(3. vás (%) + 4. Vo? (xs)+3. You (xs)) (90244024 902) = (2204) = (\ u62 -- 4 Thus, Vas () = (4403 conect Answer is (A) Auswa