Chapter 14.2, Problem 5Q

Suppose that $n=7$ paired observations, $\left(X_i,Y_i\right),$ are recorded, $i=1,2,\mathrm{...},7$. Let $p=P\left(Y_i\text{ > }{X}_i\right).$ Write out the entire probability distribution for $Y_{+},$ the number of positive differences among the set of $Y_i-X_i’s$, $i=1,2,\mathrm{...},7,$ assuming that $p=\frac{1}{2}.$ What a levels are possible for testing $H_0=p=\frac{1}{2}\text{ versus }{H}_1:p>\frac{1}{2}?$