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Q 2 . Consider the Bloom filter. Define k = number of hash functions; N = number of bits in hash table; and D =

Q2. Consider the Bloom filter. 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
=(1-kN)D
(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-)k
(c) Show that the preceding expression can be approximated by
P~~(1-e-kDN)k
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