# exponential distribution and cumulative distribution function

A common probability distribution function is the exponential, which is often used to model failure rates for products, for example batteries. It is given by:

p(x)=(lambda*e)^(-lambda*x), over all positive real numbers (0 to infinity)

In the case where lambda = 1, what is the mean value of for the exponential distribution?

(Hint – Use the expectation operator and you may need to review “integration by parts” to solve this)

What is the cumulative distribution function P(x) for this p(x)?

What is the probability that x will lie between 2 and 3 for this p(x)?