i need solve a,b,c,d,e,f,g please help me

Q1) (50 points) The Air Quality Index (AQI) is an indicator of the air quality in a particular location, computed from a combination of standardized measurements. The numerical values fall into categories that are coded by colors for easy comprehension. AIR QUALITY INDEX (AQI) CATEGORY 0-50 Good 51-100 Satisfactory Moderate Poor Very Poor 401-500 Severe 101-200 201-300 301-400 The category colors are green, yellow, orange, and red corresponding to good to severely poor air quality as shown in the figure. In areas where the atmosphere stagnated, whether by temperature inversion or geographic features such as mountains, the air quality can deteriorate rapidly. Only random weather events, such as precipitation or strong winds can refresh the air such places. A record of several years of data describing successive days of the air quality index produced the following table: Air Quality on Second Day Air Quality On First Day of Pair Green Yellow Orange Red Green 135 167 0 0 Yellow 149 152 19 0 Orange 30 0 160 80 Red 19 0 0 281 The numbers in the cells are counts of the number of times the corresponding pair occurred. For example, (Green, Green) pair occurred for 135 times, (Green, Yellow) pair occurred 167 times whereas (Green, Orange), and (Green, Red) pairs have not occurred. a) (10 points) Explain how you think these data were collected (In not more than three sentences) b) (5 points) Suppose that we observe the AQI at discrete time points. Define Xn, and write down the state space S. c) (10 points) Write down the P matrix. (When calculating the probabilities truncate them to three digits after the decimal, e.g. write them 0.2344356 as 0.234) d) (5 points) Suppose it is Monday today. Calculate the probability that the air quality will be Red on Monday and Tuesday and Poor on Wednesday. e) (5 points). Suppose that air quality is in Red category today, what is the probability that it will be in Orange category on Sunday? f) (5 points) What is the probability of having three days in Yellow category before the AQI goes into one of the other three categories? g) (10 points) Calculate the average number of consecutive days that the AQI remains in Orange category. Explain the meaning of quantity you calculate