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The life duration for a light bulb is well approximated by an exponential random variable with...

  1. The life duration for a light bulb is well approximated by an exponential random variable with a mean of 400 hours. Assume that a classroom has a projector that has a life bulb with a lifetime distribution as above, and it is used 40 hours per week. Also, for your calculations, assume that a month has exactly 4 weeks.

  1. What is the probability that you would need to replace the bulb no more than twice a year? Assume uniform usage across the year (no vacations).
  2. If the projector has a spare bulb, that automatically takes over when the first one breaks, what is the probability that the projector will function for more than 900 hours? What is the distribution of the lifetime of the projector in this case (assume it breaks only when both bulbs break)?

Hint: use CDF for calculations.

Math   Statistics-And-Probability   
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