(a) The discrete random variable X has the probability function given by: k(x+2) x=-1,0,1, 2 P(X = x) = 0 otherwise Find: (i) the constantk (ii) E00 (iii) Var(X) (iv) F(X=l) (b) The probability that a biased coin lands a HEAD is 0.45. In a trial with 12 throws, calculate: (i) the probability that the die lands a HEAD, exactly 5 times [to 4 d. p. ] (ii) the probability that the die lands 3 HEAD, less than 11 times [to 4 d.p. (iii) the mean and the standard deviation of this distribution. (0) In a Math test with a group of students, 5 students on average fail to pass. What is the probability of 6 students in the same group failing to pass? Give your answer correct to 4 decimal places