1. A lecture hall is having wiring issues, and the projector occasionally powers down randomly following an exponential distribution with rate (power downs per minute). a) A professor plans to give an 80 minute lecture. What is the power-down rate so that there is a probability of 0.05 that the lecture will not finish before the projector shuts down? b) If the lecture is only 50 minutes, how does this change the rate needed to get a probability of 0.05 of not finishing the lecture without an outage? c) Given the rates that you solved for in parts (a) and (b), what is expected value of how much time occurs between power-down events under the exponential distribution mode?.

1. 1. (18 total points) Consider the following game b) (10 points) On a single graph, graph each
player's Best Response Correspondence (technically, they are not functions). Be sure to label
your graph carefully. Please put p on the horizontal axis, and q on the vertical axis. Also, identify
the Nash Equilibrium in mixed strategies. This game has a unique mixed strategy equilibrium
where Player A chooses Top with probability p, and Bottom with probability (1- p). Also, Player B
chooses Left with probability q, and Right with probability (1q). a) ( 8 points) Calculate the values
of p and q that constitute a mixed strategy equilibrium.