GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY.

Hi,kindly reply with whole answers correct,accurate answers and step by step working.Do not skip step.Be very clear and mention about the formula for each step.Make sure the answers are correct and accurate. Be very organised with the working and systematic.Please explain to support and make it clear.

STA108

DECEMBER 2018

QUESTION 8 Let the probability distribution function of X be defined as follows. 0.4 + X x = 0,1,2,3,4 20 f ( x ) = 7.5- X x =5.6 10 0 elsewhere a) Show that f(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; f ( x ) = k(x+2) 0