(Answered) Question 1 a christmas display has 200 lights the times to

Statistics

Question: 1. A Christmas display has 200 lights. The times to failure are iid, exponential (1/10000). The display is on continuously for 750 hours (approximately one month). Determine the probability the number of lights which survive the entire period is at least 175, 180, 185, 190.

2. A critical module in a network server has time to failure (in hours of machine time) exponential (1/3000). The machine operates continuously, except for brief times for maintenance or repair. The module is replaced routinely every 30 days (720 hours), unless failure occurs. If successive units fail independently, what is the probability of no breakdown due to the module for one year?

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