For those confused like me regarding the fishing example:for part d): The number of fish caught can be found in 2 waysConsider 3 Random Variables:F: No. of fish caughtT: Time (The values that time can take)FishTime: FishingTime (The values that fishing time takes, note that this is different from Time r.v.)1) E[F] = E[F|0<T<2] * P(0<T<2) + E[F|T>2] * P(T>2)                (0.6*2)       * 1               + 1              * P(0,2) 2) E[F] = E[F|FishTime=2] * P(FishTime = 2) + E[F|FishTime>2] * P(FishTime>2)                E       * (1-P(0,2))               + 1              * P(0,2)Here E will not be = lambda * tauThis is because if he fishes for exactly 2 hours it means he will definitely not catch 0 fish.So we need to calculate the conditional pmf. That is P(catches k fish|catches atleast 1 fish)Then use this to find the new Expected value by multiplying with k and summing for k = 1, 2....Then put this for E and calculate.Gives the same answer.####[]