Is it Exponential distribution? or Geometric distribution?

The life times, Y in years of low-grade lightbulbs follow an exponential distribution with a mean of 0.7 years. A tester makes random observations of the life times of this lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise.

Part a) Find the probability that the first success occurs in the fifth observation.

Part b) Find the probability of the second success occurring in the 8th observation given that the first success occurred in the 3rd observation.

Part c) Find the probability to 2 decimal places that the first success occurs in an odd-numbered observation. That is, the first success occurs in the 1st or 3rd or 5th or 7th (and so on) observation.

Question

Sarah Rivas

Mathematics

23 November, 04:31

Is it Exponential distribution? or Geometric distribution?

The life times, Y in years of low-grade lightbulbs follow an exponential distribution with a mean of 0.7 years. A tester makes random observations of the life times of this lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise.

Part a) Find the probability that the first success occurs in the fifth observation.

Part b) Find the probability of the second success occurring in the 8th observation given that the first success occurred in the 3rd observation.

Part c) Find the probability to 2 decimal places that the first success occurs in an odd-numbered observation. That is, the first success occurs in the 1st or 3rd or 5th or 7th (and so on) observation.

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Answers (1)

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Duncan · Answer 1

I believe you use the exponential distribution to find the probability of success (say "p"). Then, you use the Geometric (p) distribution using the "p" you calculated from the exponential as your success probability. Also, in b), you use a negative binomial (which is really just a generalized geometric distribution).

Part c) Find the probability to 2 decimal places that the first success occurs in an odd-numbered observation. That is, the first success occurs in the 1st or 3rd or 5th or 7th (and so on) observation.