(a) Some species of crab regularly undergo the process of molting. This is when the crab sheds its shell and grows a new one. Dur- ing the process of molting, the crab has increased vulnerability to being killed by predators. Sketch the graph of the failure rate function r(t),t > 0, of such a crab if it (a) has increased vulnera bility to predators right after being born, (b) molts twice during its lifetime, (c) starts aging after the first molt, (d) never lives past a certain maximum age, denoted by a. Make comments in the graph about the shape of r(t). (b) The continuous random variable T has failure rate function r(t) 1+ 1,120. Compute P( TI). (c) Consider the failure rate function r(t) in discrete time for a human life (in years), and let f(t) be the pmf, t = 0,1,2,.... What can be said about the numerical values of f(115) and r(115)? (a) Some species of crab regularly undergo the process of molting. This is when the crab sheds its shell and grows a new one. Dur- ing the process of molting, the crab has increased vulnerability to being killed by predators. Sketch the graph of the failure rate function r(t),t > 0, of such a crab if it (a) has increased vulnera bility to predators right after being born, (b) molts twice during its lifetime, (c) starts aging after the first molt, (d) never lives past a certain maximum age, denoted by a. Make comments in the graph about the shape of r(t). (b) The continuous random variable T has failure rate function r(t) 1+ 1,120. Compute P( TI). (c) Consider the failure rate function r(t) in discrete time for a human life (in years), and let f(t) be the pmf, t = 0,1,2,.... What can be said about the numerical values of f(115) and r(115)