Question 4 20 marks (a) The following table shows the probability distribution of a discrete random variable X. X 0 1 2 3 4 P(X) 0.1 0.2 0.3 + k 0.15 0.05 + 100 (i) Find the value of k. Correct your answer to 2 decimal places. (2 marks) (ii) Find the expected value of X. (4 marks) Find the variance of X. (4 marks) ( b ) 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)