(a) The number of hours that a flight from London to Dublin is early or late is a random variable X whose probability density function (pdf) is given by f(x) = 1 k (9 − x 2 ) for − 3 < x < 3; 0 otherwise, where negative values correspond to the flight being early, and positive values correspond to the flight being late and where k is a constant number. (i) Find the value of the number k. (ii) Find E(X). [8 marks]
(b) Suppose X is a random variable with X ∼ N(340, 64). (i) Calculate P(334 ≤ X ≤ 348). (ii) Find x0 if P(x0 ≤ X) = 0.2206. [10 marks]
(c) The probability of correctly guessing which number shows on a rolled dice is 1/6. What is the probability of making your 4th correct guess on the 7th attempt?