Thanks, Luis!

>> How did you change the conditional probability P(W|Y) into P(W(d+y)?

This is the recursion, which works due to independence. We can use the information about whether a goal was scored in the last increment contained in the random variable Y to change the score differential in W with i-1 increments. We have to account for a difference in the score–and that associated probability–between time increments.

I fixed the LaTeX expression. The editor seems to be fragile on WordPress. Thanks a:)

]]>Also I think there is problem with your last LaTEX expression.

Thanks and stay safe.

Luis