engineers at a factory are investigating models for the life lenght of a particular component. the continuous random variable X has probability density function

f(x)= 3e^-3x for x>0

a) show that the cumulative distribution function of X is 1-e^-3x

b) show that the median value of X is 0.23, correct to 2 dp

c) write down an expression for P(X>t), where t>0. hence show that the conditional probability P(X>a + b/ X>a) is equal to P(X>b) for any a and b greater than zero

d) explain why the result in part c suggests that X is unlikely to be a fully satisfactory model