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Suppose we want to smooth the likelihood term of a noisy channel model of spelling. We are given two words, x and w, where x is the same as w, except the letter wi?1 in w has been miss typed as wi?1xi in x. Specifically, we want to apply add-one smoothing to P(x|w), the probability of typing wi?1xi instead of wi?1, where xi and wi?1 are single letters. For insertions, P(x|w)=ins[wi?1,xi]c(wi?1), where ins[wi?1,xi] is the number of times that xi is inserted after wi?1 in the corpus, and c(wi?1) is the number of times letter wi?1 appears in our corpus. Again, please note that here xi and wi?1 are individual letters, not words. What is the formula for P(x|w) if we use add-one smoothing to the insertion edit model? Assume the only characters we use are lowercase a-z, that there are V word types in our corpus, and n total characters, not counting spaces.

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