QUESTION 8 Let the probability distribution function of X be defined as follows. 0.4 + X x = 0,12,3,4 20 1 ( x ) = 7.5- X x =5,6 10 0 elsewhere a) Show that / (x) is a discrete probability distribution function. (3 marks) b) Construct the cumulative distribution function, F(x) . (3 marks) c) Calculate P(X 23). (2 marks) d) Find E(8-2X). (3 marks)QUESTION 9 ABC Company has conducted a survey to know the perception of the customer towards their new product. A mail questionnaire was distributed. The proportion of people who respond to a certain mail questionnaire is a continuous random variable X, which has the probability density function as follow; 1 (x ) -k (x + 2) 0