Let X and Y be the joint RV s representing the time till the next sneeze reexevent and the next yawn reex-event in the classroom. Assume that they are independent, and exponentially distributed with rates = 5 sneezes per hour and = 10 yawns per hour. Furthermore, let S be the RV indicating the rst sneeze reex-event or yawn reex-event.

(a) (5 points) Determine the probability that the next reex-event is a sneeze. That is, determine Pr[X < Y ]. (b) (5 points) Given that 5 sneezes already happened in the rst 20 minutes of our class period, and so far nobody yawned, determine the probability that the next reex-event is a sneeze in this situation. (c) (5 points) Given that 5 sneezes already happened in the rst 20 minutes of our class period, and so far nobody yawned. Determine the expected value of the time till the next reex-event (either a sneeze or a yawn).(provide process please)