random shortest grid walk Let $W$ be a random shortest grid walk from $(0,0) \to (20,20)$. Compute exactly

a) the expected area above or to the left of $W$,

b) the expected number of turns of $W$.

Please help, give some hints!
Hint for B: you might try to look the star and bars theorem. If you write the paths like $x^{p_1}y^{p_2}\ldots z^{p_{i+1}}$(x is to go up and y to go right) where z is x or y depending in the parity of i, you would have i changes of direction. So you are interested in how many ways you can write 20 as sum of $p_1+p_3+\ldots+p_{2k+1}+\ldots p_{t}$ and $p_2+p_4+\ldots+p_{2k}+\ldots p_{t'}$ where t and t' ara i or i+1 depending in the parity of i such that $p_j\geq 1$ for every j.
You are in Pak's course right?

Consider 11 positions between Rs, each Up take place will have 0, 1, 2...10 added area.