An engine has a piston with a surface area of 17.31 in2 and can travel 3.44 inches. What is the potential change in volume, displacement (\Delta VΔV) , of the cylinder?

$$\begin{align*}

P(Y-X=m | Y > X) &= \sum_{k} P(Y-X=m, X=k | Y > X) \\ &= \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) \\ &= \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).\end{split}$$

Explanation:

\eqalign{

 P(Y-X=m\mid Y\gt X)

   &=\sum_kP(Y-X=m,X=k\mid Y\gt X)\cr

   &=\sum_kP(Y-X=m\mid X=k,Y\gt X)\,P(X=k\mid Y>X)\cr

   &=\sum_kP(Y-k=m\mid Y\gt k)\,P(X=k\mid Y\gt X)\cr

}

P(Y-X=m | Y > X) &= \sum_{k} P(Y-X=m, X=k | Y > X) \\ &= \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) \\ &= \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).\end{split}$$