1. Each year n students of the Engineering Faculty are issued with a survey regarding their favourite topics. Each surve

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1 Each Year N Students Of The Engineering Faculty Are Issued With A Survey Regarding Their Favourite Topics Each Surve 1 (477.15 KiB) Viewed 94 times

1. Each year n students of the Engineering Faculty are issued with a survey regarding their favourite topics. Each survey contains two questions which take binary responses: The first asks students whether they like machine learning or not, while the second asks studentss whether they like maths or not. Not all students answer the questions. The results in terms of number of respondents are given below: Answers to 2nd Question: Dislike Maths Like Maths Not Answered Answers to n 11 nio nih 1st Question: Like Machine Learning Dislike Machine Learning Not Answered no1 noo noh пh1 nho nhh Table 1: Number of survey responses Let us characterise a random variable X1 with outcomes associated with machine learning preference given by x1 € {0,1}, (denoting dislike and like respectively) and a random variable X2 with outcomes associated with maths preference given by 22 € {0,1}, (denoting dislike and like respectively). We wish to learn the joint distribution, px(x1, x2) (where X = [X1, X2]T) characterised by: px(x1 = 1, X2 = 1) = 211 Px(x1 = 1,x2 = 0) = Q10 Px(x1 = 0, x2 = 1) = 201 px(x1 = 0, x2 = 0) = 200 Here a11, Q10, 201, 200 € (0,1), and (a11 + Q10 + 001 +000) = 1. (a) [6 marks) If we ignore all surveys which contain missing data then derive the maximum likelihood estimatiors of a11, Q10, 201, 200 in terms of contents of Table 2. (NB: You should handle parameter constraints using the following re-parameterisation trick: akl = where nkl E R.] ICO eti enkl