I have a little problem with this exercise.
The lifetime of a device (in years) is exponentially distributed with the parameter $λ = 0.02$.
After what time are 25% of all devices that were produced at time $t = 0$ still functional?
I have done what follows:
Let $g$ be $=0$ if the device is not functional and $=1$ if it is functional.
Now we must find $t$ so that $P(g=1)=0.25$
So we have $=0.02e^{-0.02t}=\frac{25}{100}$
so we have
$e^{-0.02t}=\frac{25}{2}$
$t=\frac{ln(\frac{25}{2})}{-0.02}$
But the result seems wrong. Where is my error?