I have the problem:
Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has mean $μ$ and variance $σ^2$.
Find $\mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T = k[(X_1-X_2)^2 + (X_3-X_4)^2]$ is an unbiased estimator of $σ^2$.
How would I go about this? I have no clue