Question

an outdoor restaurant in a summer resort closes only on rainy days finite

An outdoor restaurant in a summer resort closes only on rainy days. From past records, it is found that from May through September, when it rains one day, the probability of rain for the next day is 0.4 when it does not rain one day, the probability of rain for the next day is 0.06. (A) Draw a transition diagram (B) Write the transition matrix. (C) if it rains on Thursday, what is the probability the restaurant will be closed on Saturday? On Sunday? (A) Draw the transition diagram. Let A be the state in which it rains А No (Type integers or decimals. Do not include the % symbol in your answer.) (B) Write the transition matrix, P. Let A be the state in which it rains

Answer 1

20.9 rain next day Sol In problem we have an outdoor rutouryant in a summer resouet clous only on poiny days from pout record , May – September #lethen it rains one day; Prob of rain next day # Luthen it does not rain one day the prob. og = 0.06 Now We define 2 states {A, A'Y A state in which rains A state in which does not rain SO PAAI - Prob that rainy day to Mon Rainy day - |- PAA |-0-470.6 {PAA Prob. of Paing day to Rainy days PAA Prob that Non Rainy day to Rany day - Po 0.06 PA'A' - Prob that Non Roing day to Non Rowing day FI-PA'A = 1-0.06= 0.94 Now Part CA) kle draw a transition diagram 017 20.99 Here arrow from one state to mother state represent tois 0.05

meaching prob. in compatible Step. (6) Tromsition Prob. Matrix is a square matrice used to describe the In , Markov chain, stochastic matriac transition og a Mourbon Chain Each of it's entries is a non Mumbere reapresenting a probability Now Let P be Matrix negative real НА A 10.4 A 06 Pa PAA PAR A' 0.06 0.94 © 77 PCIf it rains Thursday, the rutauront will be closed on Saturday? 2010; kthen Rainy dlay Restaurant will cloved so Saturday must be raing day so = 0.6X0.94%0.06 +0.6x 0.06x0.4 +0.4*0.9x04 = 04/23 Similovely Thursday, the relauront will be closed on Sunday) - PAR PAM = 0.6X0.94x0.06x0.9 +0.6x0.06x0.6x0.06 +0.6X0.94 x 0.940.06 + 0.4x 0.9 x 0.4x0.4 PAA = 0.0723 PAD P(If it rains on (4) (97