Chapter 5.3, Problem 9E

Let $X_1,X_2,\mathrm{...}{X}_n$ be a random sample (of size n) from a distribution that has mean $\mu$ and variance ${\sigma }^2$.

Define $Y_1=X_1,Y_2=X_1-X_2,Y_3=X_1-X_2+X_3,\mathrm{...},Y_n={\displaystyle {\sum }_{i=1}^n{\left(-1\right)}^{i-1}{X}_i}$.

Find $E\left(Y_k\right)$ and $\mathrm{var}\left(Y_k\right)$ for $k=1,....n,$.