Suppose it has been observed that touchdowns scored in a game by your favorite football team are Poisson random variables. The rate is lambda = 4 per game. We know from the lecture that the time until the next touchdown follows an exponential distribution. Assume a football game is 60 minutes long (that is we are concerned only with the regular playing time).
1. What is the expected time in minutes until the next touchdown is scored by your favorite team?
2. What is the probability that the next touchdown will be scored in the next 10 minutes by your favorite team?
3. What is the probability that there will be no more touchdowns scored by your favorite team given that we are in the 50th minute of the game?