1. ## exponential distribution

The lifetime of a brake has an exponential distribution with mean BETA? What is the probability the
brake lasts more than twice its expected lifetime?

I would think it would be something like this. Am I close? How would I solve for two unknowns?

1 - e^(-y/BETA) = 1 - e^(-y/BETA)

2. ## Re: exponential distribution

exponential distribution w/parameter $\lambda$ has mean $\lambda^{-1}$

so your distribution has parameter $\beta^{-1}$

the CDF with parameter $\lambda$ is given as

$1-e^{-\lambda x}$ which here translates to

$F(x) = 1 - e^{-\frac x \beta}$

You want to know the probability the brakes last $2\beta$ or longer so evaluate

$1 - F(2 \beta)= e^{-2}$