# exponential and gamma distributions

The lifetime of a tubelight exponentially distributed random variable with mean=2 years. If five such tubelights are purchased for a point and used one after another, what is the probability that it will last for atleast 10 years?

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Hint: If $X_{i}$ is distributed exponentially with mean $1/\lambda$, then:
$$\sum^{k}_{i=1}X_{i}\sim\mathrm{Erlang}(k,\lambda)$$