The lifetime, in years, of a certain type of pump is a random variable with probability density function:

f(x)= {64/(x+2)^5 x>0
0 x<=0}

a. What is the probability that a pump lasts more than two years?
b. What is the probability that a pump lasts between two and four years?
c. Find the mean lifetime.
d. Find the variance of the lifetimes.
e. Find the cumulative distribution function of the lifetime.
f. Find the median lifetime.
g. Find the 60th percentile of lifetimes.