Part (a)- (3 mark) Suppose the time (in hours) taken to carryout a certain task is an r.v x having a gamma distribution with parameters =3 and =1/2. 8- The probability it takes at most 1 hour to carry out the task is; (a) 0.677 (b) 0.143 (c) 3.23 (d) 0.323 Part (b)- (2+2=4marks) The lifetime X (in hundreds of hours) of a certain type of component has a weibull distribution with parameters =1/2 and =2. 9- The expected value of X is; (a) 8 (b) 2 (c) 6 (d) 4 10- The P(X6) is; (a) 0.996 (b) 0.823 (c) 0.757 (d) 0.706 Part (c) = ( 3 marks) Let Z be a standard normal r.v. The probability of P(2.5Z0) is; (a) 0.5062 (b) 0.0062 (c) 0.5 (d) 0.4938