JE 336 OPERATIONS RESEARCH: STOCHASTIC MODELS Spring 2022 ASSIGNMENT 1 (10%) MI Due Date: March 23, 2022 (Wednesday by Midnight) Student Name Student ID 01. (40 points) The weather in a city is very difficult to predict. The weather can be very good one day and bad the other day. The metereology office tries to predict the status of weather for noon each day. The weather can be classified into three different categories as Sunny, Cloudy or Rainy. a) (10 points) Explain how we can see the state of weather as a "Random Experiment". b) (10 points) Write down the sample space of this random experiment. c) (10 points) Write down the event that the weather is either cloudy or rainy using set notation. Write down a new event that is disjoint (mutually exeusive) to the previous event. d) (10 points) What would be the appropriate observation points (epochs) of the weather? Explain. a Q2. (60 points) Consider question 1. Now, answer the following questions. a) (10 points) Explain why state of the weather at noon is a discrete-time stochastic process. b) (10 points) Explain the Markov assumption on the state of weather and discuss whether it is reasonable or not. c) (10 points) Explain the Stationarity assumption and provide a situation where the stationarity assumption is not reasonable d) (10 points) Define X, and write down the state space e) (10 points) Explain how we can estimate the one-step transition probabilities. (10 points) Provide a realization of the process (should include 5 steps) and explain this realization