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)

Probability and Statistics, Mathematics / By

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 …

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) Read More »

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

Mathematics, Calculus / By

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

1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the sum of two even integers is even. 3. Show that the square of an even number is an even number using a direct proof. 4. Show that the additive inverse, or negative, of an even number is an even number using a direct proof. 5. Prove that if m+n and n+p are even integers, where m,n, and p are integers, then m+p is even. What kind of proof did you use? 6. Use a direct proof to show that the product of two odd numbers is odd. 7. Use a direct proof to show that every odd integer is the difference of two squares. 8. Prove that if n is a perfect square, then n+2 is not a perfect square.

Mathematics, Advanced Math / By

EXPERT ANSWER

What is wrong with the following “proof” that -3 = 3, using backward reasoning? Assume that -3 = 3. Squaring both sides yields (-3)2 = 32, or 9 = 9. Therefore -3 = 3

Mathematics, Advanced Math / By

What is wrong with the following “proof” that -3 = 3, using backward reasoning? Assume that -3 = 3. Squaring both sides yields (-3)2 = 32 or 9 = 9. Therefore – 3 = 3. EXPERT ANSWER Yes, It is wrong.Because, even if the squares of two numbers equal then the two number ay not …

What is wrong with the following “proof” that -3 = 3, using backward reasoning? Assume that -3 = 3. Squaring both sides yields (-3)2 = 32, or 9 = 9. Therefore -3 = 3 Read More »