QUESTION 2

(a) The probability density function (p.d.f) for a discrete random variable X is as below: 1 ( ) (2 3) for = 1,2,3,4. P X x x x = = + 32 (i) Calculate P(X>2) (4 marks) (ii) Find E(X). (3 marks) 2 (iii) Find E(2X + 3X  1) (3 marks) (b) A manufacturer of an electronic devices product knows from past experiences that 5% of the production will have some type of minor defects that will require an adjustment. In a sample of 20 products, find the probability that (i) None will need an adjustment (3 marks) (ii) More than three will need and adjustment (2 marks) QUESTION 3 a) Suppose that K is a continuous random variable with density (1 ), for 0 1 Cx x x  < <