Let $Y_1, Y_2, Y_3$ be independent exponentially distributed random variables, with parameters $\lambda_1, \lambda_2, \lambda_3$ respectively. Why is it the case that:
I just came across this fact but I'm not sure where it comes from. I do know that if we define $Y=min(Y_1,Y_2),$ then $Y$ is an exponential random variable with parameter $\lambda_1+\lambda_2$. Is this fact related to the one above?