Final answer:
The unigram perplexity measures how well a language model predicts a sequence of words. In this case, we have a training set of 100 numbers, with 91 zeros and 1 each of the other digits 1-9. The test set consists of 10 numbers, all zeros except for one 3.
Step-by-step explanation:
The unigram perplexity measures how well a language model predicts a sequence of words. In this case, we have a training set of 100 numbers, with 91 zeros and 1 each of the other digits 1-9. The test set consists of 10 numbers, all zeros except for one 3. To calculate the unigram perplexity, we need to calculate the probability of each number occurring based on the training set and then calculate the average perplexity for the test set.
First, we calculate the probability of each digit occurring in the training set. The probability of zero is 91/100, and the probability of each non-zero digit is 1/100.
Next, we calculate the perplexity for each number in the test set. For the zeros, the perplexity is 1/probability(zero), which is 100/91. For the digit 3, the perplexity is 1/probability(3), which is 100.
To calculate the average perplexity for the test set, we sum up the perplexity for each number in the test set and divide by the number of numbers. In this case, the average perplexity is (100/91 + 100 + 100/91 + 100/91 + 100/91 + 100/91 + 100/91 + 100/91 + 100/91 + 100/91) / 10, which is approximately 1.094.