Question 4 20 marks (a) (b) The following table shows the probability distribution of a discrete random variable X. n P X 0.2 0.3+]: 0.15 ( . l) -n.-- 005 +100 (i) Find the value of 1:. Correct your answer to 2 decimal places. (2 marks) (ii) Find the expected value of X. (4 marks) (iii) Find the variance of X. (4 marks) The probability for any candidate to pass a driving test is (0.62 +). Suppose a random sample of 5 candidiates of the driving test is selected. (i) Find the probability that at least 2 candidates in the sample passed the driving test. Correct your answer to 3 decimal places. (6 marks) (ii) Let Y be the number of candidates in the sample who are able to pass the driving test. Find the mean and standard deviation of the random variable Y. (4 marks)