If you have a lamp with burning time 4000 hours. If the time goes forward until the lamp will be destroyed the exponential distribution is 3675 hours, what is the probability of a lamp to be working at least 4000 hours?
I don't know how to calculate in order to achieve the result?
I have read the document about calculation but still I don't know how to do it.
If $X$ has an exponential distribution with parameter $\lambda$ then $P[X\geqslant x]=\mathrm e^{-\lambda x}$. The time during which the lamp is working has the statistical properties of $X$ for $\lambda^{-1}=3675$ hours. Use this for $x=4000$ hours.