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 March 2016

QUESTION 3 a) Given that P(X) = P(Y [ X) = and P(X'nY) = -, calculate 5 i) P(Y) ii) P(XUY') ini) P(X'| Y') (9 marks) b) How many different ways can all the letters in the word 'HETEROGENEOUS' be arranged if the vowels have to appear together? (3 marks)C) B&C Son. Bhd. produces two types of radios, 60% are X radio and 40% are Y radio. A radio is randomly selected from a production line to check if it is malfunction. From the past data, it is known that 5% of X radios and 3% of Y radios are malfunction. Draw a tree diagram for the above situation. Find the probability of getting a malfunction radio. If a radio was inspected and found to be malfunctioned, what is the probability that it is a Y radio? (8 marks) QUESTION 4 a) The random variable X has probability distribution given in the table below X -2 -1 0 1 2 P(X =X) 0.1 0.3 0.2 C 0.1 Find the value of c. ii) P(X > 0). cumulative distribution of X. (8 marks) b) A continuous random variable X has a probability density function given by: kx :0sx