QUESTION ONE Children at a school are given weekly grade sheets, in which their effort is graded in four levels: 1 "Poor, 2 "Satisfactory", 3 "Good" and 4 "Excellent". Subject to a maximum level of Excellent and a minimum level of Poor, between each week and the next, a child has: . a 20 per cent chance of moving up one level. a 20 per cent chance of moving down one level. a 10 per cent chance of moving up two levels. .a 10 per cent chance of moving down two levels. Moving up or down three levels in a single week is not possible. Required: i. Draw a transition diagram to represent this process (2 marks) ii. Write down the transition matrix of this process. (3 marks) Children are graded on Friday afternoon in each week. On Friday of the first week of the school year, as there is little evidence on which to base an assessment, all children are graded "Satisfactory". iii. Calculate the probability distribution of the process after the grading on Friday of the third week of the school year. (5 marks) QUESTION ONE Children at a school are given weekly grade sheets, in which their effort is graded in four levels: 1 "Poor, 2 "Satisfactory", 3 "Good" and 4 "Excellent". Subject to a maximum level of Excellent and a minimum level of Poor, between each week and the next, a child has: . a 20 per cent chance of moving up one level. a 20 per cent chance of moving down one level. a 10 per cent chance of moving up two levels. .a 10 per cent chance of moving down two levels. Moving up or down three levels in a single week is not possible. Required: i. Draw a transition diagram to represent this process (2 marks) ii. Write down the transition matrix of this process. (3 marks) Children are graded on Friday afternoon in each week. On Friday of the first week of the school year, as there is little evidence on which to base an assessment, all children are graded "Satisfactory". iii. Calculate the probability distribution of the process after the grading on Friday of the third week of the school year