Q3. (a) Table 2 shows the probability distribution for a discrete random variable X. Table 2 X 2 3 4 P( X =x) 0.25 0.45-2a 0.22 0.44-a Find (i) the value of a, (2 marks) (ii) E(X) and Var (X), (4 marks) (in) PIXzLE( x ). (2 marks) (iv) E(1-5X) and Var(3X-5). (2 marks) (b) A continuous random variable Xhas the probability density function defined by f (x) =6x(1-x), OSx51, 0 , otherwise. (i) Find the mean and variance. (6 marks) (ii) Given P(X > a) =0.15. Show that 40a -60a +17=0. (4 marks)