The lifetime distribution of members of a certain stationary population of insects has probability density function

where x is measured in days.

(a) Identify the lifetime distribution of an individual and hence write down the expectation of life at birth.

(b) Find the life table function Q(x) for members of this population.

(c) Find the median lifetime for insects in this population.

(d) Find the mean age of insects in this population.

(e) What proportion of insects live for more than 10 days?
 

1 25 f(x) = rs re=z/50, r 0, x