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 â€“ Use the expectation operator and you may need to review â€œintegration by partsâ€ 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)?