Please answer this question . I need tour help.This can use hospital rule.

1. The Weibull distribution can be used to model many real life situations. (a) The lifespan of organisms is one of such situations. According to the Weibull distribution, the likelihood that an organism dies at the age of t is proportional to f (t ) = th-1 exp (-t*), +20, where k > 0 is a constant that depends on the type of organism being studied, and on the environment that it is living in. (i) Prove that for all values of k, f(t) - 0 as too. (ii) For what values of & does f converge to a finite value as t -+ 0? Show your work. (ii) Describe the interpretation of the results in parts (i) and (ii). L [ 20 marks ] (b) On the other hand, according to the Weibull distribution, the likelihood that a time t elapses between the end of one forest fire and the start if the next one is also proportional to f (t ) = th-1 exp (-1*), +20. Further, it can be shown using the laws of probability that the probability of a second forest fire starting at any time following the first is proportional to So f(t) dt. Show that the integral is convergent for any value of k 2 1. [5 marks ]