Which one is not a condition of Poisson model(a) the probability of having failures in a small time interval is constant(b) the probability of having success more than one in a small time intervalis very small(c) the probability of having success in this time interval is independent oftime ‘t’ as well as earlier success(d) the probability of having success in a small time interval (t, t+td) is Kt fora positive constant k

The Poisson distribution can model a system where two events can occur simul- taneously. a. True b. False

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

Select all that applyAn experiment satisfies a Poisson process if:Multiple select question.the number of successes within a specified time or space interval equals any integer between zero and infinity.the probability of success in any interval is proportional to the size of the interval.the probability of success in any interval is the same for all intervals of equal size.the number of successes counted in nonoverlapping intervals are dependent.

For a Poisson process, we define the number of '' achieved in a specified time or space interval as a Poisson random variable.

The number of accidents (𝐴) at an intersection is counted for a 12-hour period. The number of accidents follows a Poisson distribution with a parameter value of 2.Calculate the probability that there will be no accidents in a 1-hour period.