Your Perfect Assignment is Just a Click Away

Starting at $8.00 per Page

100% Original, Plagiarism Free, Customized to Your instructions!

glass
pen
clip
papers
heaphones

Computing Probabilities Sorting Lists Algorithms & True Statements Worksheet

Computing Probabilities Sorting Lists Algorithms & True Statements Worksheet

Question Description

please see attached for questions

  1. Here are two (simpli??ed) versions of Roulette. Compute the probabil- ities of losing in each.
    1. (a) Las Vegas roulette. There are 38 (uniformly random) outcomes: two green numbers 0 and 00, and 36 red and black numbers 1 to36 (half red, half black). You bet on a red or black color (say red). You then win if you get a red number, and lose if you get a non-red number. What’s the probability that you lose?
    2. (b) Monte-Carlo roulette. There are 37 (again, uniformly random) outcomes: 0 is green, and 36 red and black numbers 1 to 36(again half red, half black). You bet on a red or black color (say red). You then win if you get a red number, and lose if you get a black number. If you get the green 0, you get a special reroll, where if you get a red then you get your money back (so you don’t win but don’t lose either), but you lose if you get a green or black on the reroll. What is your probability of losing?

    Then, comment on the values themselves.

  2. Suppose you have 15 people coming together to form a committee of5 people. 6 out of 15 of the people are spies. What’s the probability that at least half of the committee are spies?
  3. True or false? (Warning: as in all my problems, you need to explain your answers to get any credit.)(a) (Z/6Z)? has a primitive root. (b) (Z/13Z)? has a generator. (c) (Z/15Z)? has a generator.
  4. Similar to Di??e-Hellman, here’s the ??Zhang key-exchange??:?? We pick a big prime p and a generator g.?? Alice has a secret a ? Z/(p ? 1)Z. 1
  • ?? Bobhasasecretb?Z/(p?1)Z.
  • ?? Alice sends ga to Bob. Bob sends gb to Alice.
  1. (a) Show that a key is indeed exchanged; that is, Alice and Bob can both compute g?a?b (mod p).
  2. (b) Showthatthiskey-exchangeisverybadcomparedtoDi??e-Hellman.
  1. How fast (big O notation is enough) can you check if two lists of nintegers each has at least one integer in common? (hint: sorting a list of n integers ?? meaning putting them in order, takes O(n log(n)) time with the best algorithms we have).
  2. Suppose g is a generator for (Z/nZ)?. Show that if x+y = 0 (mod ?(n)), then gx and gy are inverses (of each other). Is the converse of this state- ment true?

"Place your order now for a similar assignment and have exceptional work written by our team of experts, guaranteeing you A results."

Order Solution Now

Our Service Charter


1. Professional & Expert Writers: Eminence Papers only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Eminence Papers are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Eminence Papers are known for the timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Eminence Papers, we have put in place a team of experts who answer all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime.