Given a random variable with probability distribution function defined as below: f(x) = a(15 -x) , x= 2,4,6,8,10 0 otherwise (a) Find the value of a. (5 marks) (b) Sketch the graph of the probability distribution function of x. (5 marks) (c) Find the probability that X is less than or equal to 6. (3 marks) (d) Calculate the mean and standard deviation of X. (6 marks) (e) E(10X + 20). (3 marks) (f) Var(2X - 12)