2. Consider the Bloom filter discussed in Section 3.3. Define k = number of hash functions; N=number of bits in hash table; and D = number of words in dictionary. a. Show that the expected number of bits in the hash table that are equal to zero is expressed as * = (*) b. Show that the probability that an input word, not in the dictionary, will be falsely accepted as being in the dictionary is P = (1-0) c. Show that the preceding expression can be approximated as P = (1 – e *DIN)

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The objective of this question is to test the student’s understanding of Bloom filters and their applications in computer science. Specifically, the question requires the student to derive three different expressions related to Bloom filters: the expected number of zero bits in the hash table, the probability of false positives, and an approximation of the false positive probability.