The number of minutes that a flight from Dublin to Cork is early or late is a random variable whose probability density function (pdf) is given by 36-12 f(x) = { 30+ for - 6 < x < 6; k 0 otherwise, where negative values correspond to the flight being early, and positive values cor- respond to the flight being late. (i) Find the value of the number k. Find the probability that the flight will be (ii) Between 4 and 12 minutes late. (iii) Between 1 and 3 minutes early. (iv) At least 2 minutes late. (v) Find E(X) and V(X). (1 bookmark) P Show transcribed image text