Name: The total test time is estimated as 50 minutes, but you may stay afterwards and work on the test for as long as you would like (say, up to an additional hour) since the room is free then.
For multiple choice questions, also write a brief (1-2 sentence) explanation of why the answer is correct. The parenthesized numbers after each question number give the relative point value of each question.
(5) The forward recursion to compute model likelihoods can be expressed as
where means the sequence of acoustic vectors , the notation means the state at time n with category , and where there are L different state categories.
As it is commonly implemented, however, it is often expressed as
Show the steps necessary to go from the first formulation to the second. For each step say whether any assumptions are required for the equality, and if so, say what they are.