Let X be a random variable with the density function fx kex

Let X be a random variable with the density function f{x) = ke^-x for 0 LE x LE 4 and 0 otherwise be the time after which certain ball bearings are worn out (x is time measured in years). Find the appropriate value of k. Find the probability that a bearing will last at least 1 year. Find the mean mu, and the variance sigma^2. ( You need to use integration by parts).

Solution