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📗 (Fall 2018 Midterm Q11, Fall 2017 Final Q20) There are two biased coins in my pocket: coin A has \(\mathbb{P}\left\{H\right\}\) = , coin B has \(\mathbb{P}\left\{H\right\}\) = . I took out a coin from the pocket at random with probability of A is . I flipped it twice the outcome is . What is the probability that the coin was ?
📗 Answer: .
📗 (Fall 2018 Midterm Q12) You have a vocabulary with word types. You want to estimate the unigram probability \(p_{w}\) for each word type \(w\) in the vocabulary. In your corpus the total word token count \(\displaystyle\sum_{w} c_{w}\) is , and \(c_{"zoodles"}\) = . Using add-one smoothing \(\delta\) = (Laplace smoothing), compute \(p_{"zoodles"}\).
📗 Answer: .
📗 (Fall 2017 Midterm Q1) A traffic light repeats the following cycle: green seconds, yellow seconds, red seconds. A driver saw at a random moment. What is the probability that one second later the light became ?
📗 Answer: .
📗 (Fall 2017 Midterm Q2, Fall 2014 Final Q3) Let \(A \in\) and \(B \in\) . What is the least number of probabilities needed to fully specify the conditional probability table of B given A (\(\mathbb{P}\left\{B | A\right\}\))?
📗 Answer: .
📗 (Fall 2017 Midterm Q7, Fall 2016 Final Q4) In a corpus with word tokens, the phrase "San Francisco" appeared times. In particular, "San" appeared times and "Francisco" appeared . If we estimate probability by frequency (the maximum likelihood estimate), what is the estimated probability of P(Francisco | San)?
📗 Answer: .
📗 (Fall 2017 Final Q1) According to Zipf's law, if a word \(w_{1}\) has rank and \(w_{2}\) has rank , what is the ratio \(\dfrac{f_{1}}{f_{2}}\) between the frequency (or count) of the two words?
📗 Answer: .
📗 (Fall 2017 Midterm Q6) \(B\) is the boolean whether you have the bird flu or not. \(H\) is the boolean whether you have a headache or not. Let \(\mathbb{P}\left\{H = 1\right\}\) = , \(\mathbb{P}\left\{B = 1\right\}\) = , \(\mathbb{P}\left\{H = 0 | B = 1\right\}\) = . Given that you have the bird flu, what is the probability that you have headache?
📗 Answer: .
📗 Go to Google Ngram viewer: Link. Find an old phrase (two or more words) that is used less over time. Use the period between 1800 and 2019. Copy the phrase to Piazza: Link
📗 The phrase is: .
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📗 Answer: .
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