ECS708 Machine Learning
代考机器学习 Define the joint probability p (A,B) and the conditional probability p (A|B).You may want to use a diagram/sketch.
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Answer FOUR questions
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Question 1 代考机器学习
a) Define the joint probability p (A,B) and the conditional probability p (A|B) . You may want to use a diagram/sketch. Give the formula that relates them.[4 marks]
b) Give the relation between the joint probability P ( X, Y) and the probabilities P (X ) and P (Y ) that holds in the case that X and Y are independent random variables. Give the condition that holds when X and Y are uncorrelated. Are these conditions the same?[4 Marks]
c) Show that the expected value of the sum of two independent random variables X and Y is equal to the sum of the expected values of X and Y. That is, show that E{X+ Y }= E{X }+E{E+Y}.
You may show it either for continuous or discrete variables. (Hint:You need to work with the joint probability P(X ,Y )).[6 Marks] 代考机器学习
d) An IT worker works from home 2 days a week. When she works from home there is a 30% chance she will NOT answer an email within an hour, 10% chance that she will not answer an email within two hours, and it is certain that she will answer all the emails within the day.When she is at office, there is a 50% chance she will NOT answer an email within one hour,10% chance that she will not answer an email within the two hours, and it is certain that she will answer all the emails within the day.
i.If you send her an email, what is the probability that she will answer within 2 hours?
ii.Given that she hasn’t replied to your email within 1 hour, what is the probability that she is working from home? Does the information that she hasn’t answered the email within 1 hour makes it more or less likely that she works from home?[11 Marks]
Question 4 代考机器学习
a) With a help of a diagram explain the main principles of a first-order Markov Model. Explain what is meant by the term ‘’first-order”. What are the differences with a hidden Markov model(HMM)? In your answer, define the states ωi , the symbols vk , and the matrices A =[aij] and B=[bjk].[6 marks]
b) The decoding problem can be stated as follows: Given an HMM and a sequence of observation symbols V1:T determine the most likely sequence of hidden statesω1:T.What are the other two types of problems that arise in the context of HMMs?[6 marks] 代考机器学习
c) Describe an algorithm that solves the decoding problem, as this is described in part (b). What is the name of this algorithm?[13 marks]
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