h2 maths sampling

i was trying to figure out , if the qn is: S(x-20)=30, and S(x^2 = 21300), n=50, how do you go about solving the unbiased est of miu and variance?

and what happens for the other way around? [S(x)=30 and S(x-20)^2=21300]

thanks!

S(x-20) means that each data point is reduced by 20 .. to get Sx just add 20X50 to 30 .. Once you have Sx just apply the formula

erm, i dont quite get it. to go about solving the unbiased est of miu: (Sx/n= 30/50+20=20.6 right?)

i dont know how to apply the formula towards working the variance out, as the variable for both is different...

can anybody help?

let u = x - 20

E(u) = E(x -20)

E(u) = E(x) -20

E(x) = E(u) + 20

unbiased estimate of miu = E(x) = E(u)/n + 20 = 30/50 + 20 = 20.6

Case 2 for S(x-20)^2:

Var(u) = Var(x-20)

Var(u) = Var (x)

unbiased estimate of sigma^2 = 1/ 49 x ( 21300 - 30^2 / 50)

Case 3: If S(5x-20)^2 = 21300 :

Var (u) = Var (5x -20)

Var (u) = 25 Var (x)

Var (x) = 1/25 Var (u)

unbiased estimate of sigma^2 = 1/25 x (1/ 49) x (21300 - 30^2 / 50)