Completed as soon as possible.

I need help with this question as this is my first introduction to this concept. I don't have any other experience with this subject other than the accompanying lecture for this assignment. I've included my current work below.

3 The chain rule and Markov assumption Problem Using the chain rule, write out the probability for the sentence colorless green ideas sleep furiously. Then, write out the formula using a second-order Markov approximation. Hint The formulas are a product of several probabilities. You haven't been told possible values for P(colorless), etc., so you can only give formulas, not an actual probability. Solution The chain rule formula is P(colorless green ideas sleep furiously) = P(colorless) . P(green | colorless) P(ideas | colorless green) . P(sleep | colorless green ideas) P(furiously | colorless green ideas sleep) and the second-order Markov approximation is given by P(colorless green ideas sleep furiously) = P(colorless)- P(green | colorless) . F(ideas colorless green) - P(sleep | green ideas) - P(furiously | ideas sleep).The chain rule permits us to compute joint probabilities from conditional probabilities or vis versa. For two random variables A and B, it says that: P( AAB) = P(A | B) . P(B) = P(B | A) . P(A) (6) More generally, we can write: P(A, A . . . AA.) = P(A, ) . P(A2 | A1 ) . P(As | A, A A2) . . . . P(A,, | AT A;). (7)Problem Daft Punk's 2001 single "Harder, Better, Faster, Stronger\" has the following lyrics (repeated several times}: 1work it make it do it makes us harder better faster strong work it harder make it better do it faster makes us stronger more than ever hour after hour work is never over Compute the maximum likelihood probability of the phrase work is never over using a rstorder Markov approximation. Solution The formula is P(work is never over) m P(work) - P(is | 1work) - P(never | is} - P(over I never} and lling in maximum likelihood probabilities we obtain 3 1 1 1 I P(vork is never over) m ...... : m .0294. 34 3 1 1 34 2 Language models Problem Rammstein's 1997 German-language single "Du Hast" consists of the following (case- folded) lyrics, repeated twice: du du hast du hast mich du du hast du hast mich du du hast du hast mich du du hast du hast mich du du hast du hast mich du hast mich du hast mich gefragt du hast mich gefragt du hast mich gefragt und ich hab nichts gesagt willst du bis der tod uns scheidet treue sein fur alle tage nein nein Compute the maximum likelihood probability of the phrase du hast mich gefragt 'you asked me' according to a second-order Markov model