Finding the Bias and Variance of an estimator of Beta?

Question

So basically, the estimator is a slope of the highest and lowest values. $(Y_7-Y_1)/(X_1^7-X_1^1)$

I already calculated the unbiasedness by since $E(X_1^7) = u_x$ and the same for Y. However, I'm having trouble figuring out how to calculate the variance for this.

Can someone please help me out/get me started? Much appreciated

Answer 1

Note that $Y_i$ are iid $\sigma^2$ and $X_i$ are non-random so $Var(\dfrac{Y_7-Y_1}{X_7-X_1})=\dfrac{2\sigma^2}{(X_7-X_1)^2}$