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In a room, a lamp must be constantly turned on. As soon as it stops working, it is immediatly switched for a new one. Suppose that the lifetime of a lamp can be approximated by an exponetial distribution with average lifetime of 5 days. How many lamps are necessary for the probability that they are sufficient for 30 days be at least 0.95?

Well, since the average lifetime is 5 days, one can find that the parameter $\lambda = 1/5$. The only tought i had so far on this question was to partionate the interval $[0,30]$ and calculate the indepent probability that lamp $1$ survives interval $[x_1,x_2]$, ... , lamp $n$ survives from $[x_n,30]$. But it doesn't seems a good way.

Any help?

user2345678
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1 Answers1

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You take $\int e^{-\lambda\dot t}$ and get 0.5 for $t=5d$ if - which I'm not sure about - $\lambda = \frac{1}{5}$. Then you find t so that the integral evaluates to 0.95, then $\frac{30}{t}$ should be your answer.

vectorious
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