Assume that when the German plays Hungary in soccer, each team scores independently as a homogeneous Poisson process with rates $\lambda (\text{Germany}) = 1$ and $\lambda(\text{Hungary}) = 3$ goals per game.
a) Expected number of total goals in a single game.
b) Expected number of total goals scored in the first half, given that $2$ total goals were scored in the entire game.
c) Expected number of goals Germany scored in the entire game, given that $2$ total goals were scored in the first half.
What I really need help with is getting the formulas for parts b & c. I'm having difficulty forming what the Expectation formula should be.
