c programming

Problem 1 : Hashing (3\%) Bloom filter consists of m bit of memory and h uniform and independent hash functions f1,,fh. Each fi hashes a key k to an integer in the range [1,m]. Initially all m filter bits are zero, and the differential index and file are empty. When key k is added to the differential index, bits f1(k),,fh(k) of the filter are set to 1 . When a query of the type "Is key k in the differential index?" is made, bits f1(k),,fh(k) are examined. Assume that there are u records stored in the bloom filter. The probability of a false positive is P(h)=(1(11/m)uh)h Problem By differentiating P(h) with respect to h, show that P(h) is minimized when h=(loge2)m/u. ( Write a program to validate the result shown in the problem by investigating P(u) with various h's. )