DURATION :1 HOUR 15 MINUTES [TOTAL: 35 MARKS] ANSWER ALL QUESTIONS. ALL STEPS MUST BE SHOWN CLEARLY. 1. Suppose that a discrete random variable X has the following cumulative distribution function x+1 F(x) =1-(i) ,x = 0,1,2,... Find P\" =4) (3 Marks) 2. An experiment consists in injecting a virus to three rats and checking if they survive or not. It is known that the probability of surviving is 0.5 for the first rat, 0.4 for the second and 0.3 for the third. Find the mean and the standard deviation of X where X is the number of surviving rats. (7 Marks) 3. Let X is a continuous random variable with the following cumulative distribution function 0 x2 Suppose that B is the event that is . Calculate the probability . (1 0 Marks)