Per snapshot below, why is the yellow box coming into use? Why is it being used? What is it? Basically I have no idea what why the idea of the yellow box is brought up. Thank you. No one liner answers please. Solution T and N(T) both are random variables. E (N(t)|T=t) will give you the expected value of N(T) when T has the value t. So we are keeping T fixed and varying N(T) for T=t and calculating the expected value. Then to calculate E(N(T)) we are varying T and calculating the expected value of E(N(t)|T=t).