Deux bus A et B partent du même arrêt "MAIRIE" à 10h00.Le bus A met 45 minutes pour faire sa tournée, le bus B met 54 minutes.A quelle heure se retrouveront-ils en même temps à l'arrêt "MAIRIE" la prochaine fois?

Répondez aux questions suivantes au négatif :i. Odile, a-t-elle encore pris le bus?ii. Ont-ils invité tout le monde à la soirée?iii. Vois-tu quelque chose de spécial au magasin?iv. A-t-il bu de l’eau et du jus?v. Est-ce que tout reste le même?

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Excluding stoppages , the speed of the bus is 60 kmph and including stoppages the speed is 45 kmph. For how many minutes does the bus stop per hour ?

Excluding stoppages , the speed of the bus is 60 kmph and including stoppages the speed is 45 kmph. For how many minutes does the bus stop per hour ?20 min40 min25 min15 min30 min

Question 1. [9 marks]. Arrivals of the Number 1 bus at a particular bus stop form aPoission process with rate parameter λ1 and arrivals of the Number 2 bus at the samebus stop form a Poisson process with rate parameter λ2. The two Poisson processes areindependent.(a) What is the probability that precisely 4 buses (of type Number 1 and/or Number 2)arrive in the time interval [0, t]?(b) What is the probability that exactly 3 Number 2 buses pass while I am waiting for aNumber 1 bus?(c) When the maintenance depot goes on strike half the buses break down before they reachmy stop. What then is the probability that not a single bus passes in the time interval[0, t].When answering each of parts (a), (b) and (c) you should briefly explain your reasoning.Hints: (i) Recall that ∫ ∞0xα−1e−βxdx = Γ(α)βα ,where the gamma function Γ(·) is such that, for a positive integer n, Γ(n) = (n − 1)!(ii) In part (c) you may assume that thinning has taken place, as defined in the lecture notes