Suppose that we have three engines which we turn on at time 0.

Question

Each engine will eventually fail, and we model each engine's lifetime as exponentially distributed with parameter lambda.
One of the engines will fail first, followed by the second, and followed by the last.
Let T1 be the time of the first failure, T2 be the time of the second failure, and T3 be the time of the third failure.

1. Determine the PDF of T1.
for t>0,

f_T1(t) = ?

Answer 1

3*lambda*exp(- 3*t*lambda)