# Mathematics

## 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)

EXPERT ANSWER 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 …

## Evaluate Z 1 0 Z 5 5y 2e x 2 dx dy

Evaluate Z 1 0 Z 5 5y 2e x 2 dx dy EXPERT ANSWER

## Find volume of the given solid.Bounded by the coordinate planes and the plane 3x + 2y + z =6.This is a double integration problem.

Find volume of the given solid. Bounded by the coordinate planes and the plane 3x + 2y + z =6. This is a double integration problem. EXPERT ANSWER It is supposed to be

## Rewrite the following integral using the indicated order of integration and then evaluate the resulting integral. 5 0 8x + 8 SS S dy dx dz in the order dz dx dy 0 -1 0 5 0 8x + 8 H SS S s dz dx dy = dy dx dz = 0 -1 0 (Simplify your answer.) Rewrite the following integral using the indicated order of integration and then evaluate the resulting integral. 1/16 -x² (16 x² 了了了 dy dz dx to dz dy dx 0 0 T7 TT.II 1 1/16-x² / 16 x² dy dz dx = dz dy dx 0

EXPERT ANSWER The process of changing the order of integration involves rewriting the integral with the new order of variables and adjusting the limits of integration accordingly. The new order of integration should not affect the final result of the integral as long as the limits are properly adjusted