The life times, Y in years of a certain brand of lowgrade
lightbulbs follow an exponential distribution with a mean
of 0.75 years. A tester makes random observations of the life
times of this particular brand of 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 to 3 decimal places that the first success
occurs in the fifth observation.
Part b)
Find the probability to 3 decimal places 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.
