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The following questions may appear as quiz questions during the lecture. If the questions are not generated correctly, try refresh the page using the button at the top left corner.
📗 [4 points] Given the following transition matrix for a bigram model with words "", "" and "": . Row \(i\) column \(j\) is \(\mathbb{P}\left\{w_{t} = j | w_{t-1} = i\right\}\). What is the probability that the third word is "" given the first word is ""?
📗 Answer: .
📗 [4 points] Given the following transition matrix for a bigram model with words "I" (label 0), "am" (label 1) and "Groot" (label 2): . Row \(i\) column \(j\) is \(\mathbb{P}\left\{w_{t} = j | w_{t-1} = i\right\}\). Two uniform random numbers between 0 and 1 are generated to simulate the words after "I", say \(u_{1}\) = and \(u_{2}\) = . Using the CDF (Cumulativ Distribution Function) inversion method (inverse transform method), which two words are generated? Enter two integer labels (0, 1, or 2), not strings.
📗 Answer (comma separated vector): .