(a)The density function for a random variableX is given by 02 ()4 = X ()32 Kxxx fx i.Determine the value ofK. 0 otherwise ii.CalculatePX(01.<<) iii.Calculate PX(>1.75.) choice of breakfast is independent from guest to guest. (a)at most 12 of these guests require a continental breakfast ii.On a particular morning when there are 50 guests, each occupying a single room, i.On a particular morning there are 16 guests, each occupying a single room on the iv.Calculate PX(<0.9.) (b)A hotel has 50 single rooms, 16 of which are on the ground floor. The hotel offers guests ground floor. Calculate the probability that exactly 5 of these guests require a cooked breakfast. the choice being made are 0.45, 0.25 and 0.30 respectively. It may be assumed that the determine the probability that, (a)the mean and for the number of these guests requiring breakfast. (b)more than 10 but fewer than 20 of these guests require no breakfast. iii.When there are 40 guests, each occupying a single room, calculate a choice of a cooked breakfast, continental breakfast or no breakfast. The probabilities of (b)the standard deviation for the number of these guests requiring breakfast.