(15 points) Let X and Y be the joint RVs representing the time till the next sneeze reflex-event and the next yaun reflex-event in the classroom. Assume that they are independent,and exponentially distributed with rates A = 5 sneezes per hour and = 10 yawns per hour.Furthermore, let S be the RV indicating the first sneeze reflex-event or yaum reflex-event. )(5 points) Determine the probability that the next reflex-event is a sneeze. That is,determine Pr[X <Y. (5 points) Given that 5 sneezes already happened in the first 20 minutes of our class period, and so far nobody yawned, determine the probability that the next reflex-event is a sneeze in this situation. (5 points) Given that 5 sneezes already happened in the first 20 minutes of our class period, and so far nobody yawned. Determine the expected value of the time till the next reflex-event (either a sneeze or a yawn).

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15 points let x and y be the joint rvs representing the time till the

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(15 points) Let X and Y be the joint RVs representing the time till the next sneeze reflex-event and the next yaun reflex-event in the classroom. Assume that they are

independent,and exponentially distributed with rates A = 5 sneezes per hour and = 10 yawns per hour.Furthermore, let S be the RV indicating the first sneeze reflex-event or yaum reflex-event. )(5 points) Determine the probability that the next reflex-event is a sneeze. That is,determine Pr[X