AI代写

MAST30001 Stochastic Modelling MAST30001 Stochastic Modelling Lecturer: Mark Holmes 1 Stochastic modelling We study a random experiment in the context of a Probability Space (Ω,F ,P). Here, I Ω is the sample space – the set of all possible outcomes of our random experiment, I F is a sigma-field – a collection (with certain properties)

MAST30001 Stochastic Modelling 1. Discrete time Markov chains Discrete-Time Markov Chains A sequence (Xt)t∈Z+ of discrete random variables forms a DTMC if P(Xt+1 = xt+1|Xt = xt ,Xt−1 = xt−1, · · · ,X0 = x0) =P(Xt+1 = xt+1|Xt = xt), (1) for all t, x0, . . . , xt+1 such that the left

MAST30001 Stochastic Modelling Tutorial Sheet 1 1. A box has 3 drawers, one contains two gold coins, one contains two silver coins and the last drawer contains one gold coin and one silver coin. Assume that one drawer is selected randomly and that a randomly selected coin from that drawer turns out to be gold.