a shipment of goods contains two containers, one container has 300 units and the other container has 700 units. A supervisor checks 30 units in the first container and he finds $X_1$ broken units and 70 units in the second container where he finds $X_2$. broken units. which of the following estimators are the best?
$$p_1 = (X_1+X_2)/100 $$ $$p_2 = (3X_1+7X_2)/580 $$
According to the solution $Var(p_1) < Var(p_2)$ , but HOW?
here is what i did.
EDIT: removed because it was nonsens
EDIT2: ASSUME THAT I AM STUPID, explain it to me like I am a piece of cabbage, I dont "get" hints.
EDIT: After some days of work and reading I found out that everything is perfectly solvable if I write $$X_1=30x$$ and $$X_2=70x$$ and solve for var(x).... Thanks noone here I guess... I dont know why you couldnt help me with that, you probably have alot more experience with this.
Hint: $Var(a X_1 + b X_2) = a^2 Var(X_1) + b^2 Var(X_2)$
Does smaller variance always imply better estimator?