Three system components are connected in series (so the system fails if any one of them fails). The lifetimes of the components are independent random variables exponentially distributed with parameter λ. The system fails after 10 days
I'm trying to find the method of moments estimate of $\lambda$ and I need to find the PDF first. It seems to be similar to a binomial but I can't figure it out. I was given the PDF but I need an explanation.
$$f(t) = \binom{3}{1} \lambda e^{-\lambda t}(e^{-\lambda t})^2 = 3\lambda e^{-3\lambda t}$$