Describe a procedure that takes as input two integers a and b such that 0 < a < b and, using fair coin flips, produces as output heads with probability a/b and tails with probability (b – a)/b. Give a bound on the expected number of coin flips, which should be O(1). (Hint: Represent a /b in binary.)

Q: a) You are trying to send a message to your friend, and as usual, Eve is trying to decipher what the…

A: Given a problem and we need to prove encryption and decryption using E(x) and D(y)

Q: What is the probability that the below-given f(x, y, z) will return 1? f(x, y, z) = a +ỹ +x. z( x.…

A: answer : The given function will return 1 , the probability of this will be 6 / 8 = 0.75    I…

Q: The goal of this exercise is to work thru the RSA system in a simple case: We will use primes p =…

A:

Q: 2.Suppose a | b and a | c, then it follows that there are integers s and t with b = as and c = at.…

A: 2. a | b it means that if b divides a then it give the reminder 0 and quotient value is integer. So…

Q: Let A = {x ∈ Z : x ≤ 3} and let B = {x ∈ Q : x2 = 9}. Is B ⊆ A? Give a brief reason for your answer.

A: True

Q: find_solvable_blackout_equation(num_tries, n, pct_per_digit): Takes one positive integer, one…

A: from blackout_utils import * import random   OPERATIONS = ['^', 'x', '/', '+', '-']   def…

Q: . Consider an impulse response h[n] such that h[n] = 0 for n M, and h[n] =−h[M − n] for 0 ≤ n ≤ M…

A:

Q: b) Use the above consequence to show that for random variables X and Y taking finite many values,…

A: Answer : X and Y are independent.

Q: You are given the following data: t = [ 0 .1 .499 y = [0 .06 .17 .5 .6 1.0 1.4 1.5 1.899 1.9 2.0 ]…

A: MATLAB is a proprietary multi-paradigm programming language and computing environment developed by…

Q: For the boolean function f given in the table below, which of following gives correct canonical form…

A: Based on the options it is evident that the Boolean function has not been reduced so, In Sum of…

Q: Classify the following polynomials as either primitive, irreducible, or composite by writing either…

A: Hi there, Please find your solution below, I hope you would find my solution useful and helpful.…

Q: What type is inferred for a, ß, and for the variable xs? let хyz (a : a) : В %D let rec abc a =…

A: SUMMARY: - hence, we discussed all the points.

Q: Let f(n) and g(n) be positive functions over the natural numbers. For each of the following claims…

A: Given asymptotic notation correct or disprove

Q: Implement the function by simplifying and creating a truth table. F(W,X,Y,Z)= ((W^X)) | (~(Y&amp;Z))…

A: The given function is: F(W,X,Y,Z)= ((W^X)) | (~(Y&amp;Z)) where ^ (XOR), | (OR), ~ (inverse) and…

Q: Let A = {c, e,j, 1, s, u, y, z}, which of the following is true? There may'be more than one correct…

A: A={c ,e ,j ,l ,s ,u , y, z} True answers are: A. Φ ⊆ A D. {l,y,s,u} = {u,s,l,y} E. {l,y,s,u} ⊆ A F.…

Q: Ql: prove using algebraic method that ABC + ĀBC + ABC + ABC = C Q2: Draw the circuit of the…

A: 1.) Algebraic Method

Q: Give interpretations to prove that each of the following wffs is not valid: a. Ex)A(x) ^ (Ix)B(x) →…

A: a. (∃x)A(x) ∧ (∃x)B(x) → (∃x)[A(x) ∧ B(x)] This wff is invalid. Since, the existential quantifier…

Q: Given f(x)=x2+6x and g(x)=1−x2, find f+g, f−g, fg, and fg.    Enclose numerators and denominators…

A: f(x)= x2 + 6x  g(x) = 1 - x2  We have to find :-                  1 ) f + g  or f(x) + g(x) 2) f - g…

Q: (a) Show that 3x(Px x Px). (b) Show that {Qx,V y(Qy → Pz)} EX Px.

A: The solution for the above-given question is given below:

Q: For each of the following pairs of functions f(n)f(n) and g(n)g(n), determine whether Ofn))=0(g(n)).…

A: I have provided the answer with justification below.

Q: Show that each of these conditional statements is a tautology by using truth tables. c)¬p→(p→q)…

A: Note: A Statement is Tautology, when it is true for all the possible input combinations in Truth…

Q: Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9},…

A: Given Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and…

Q: Find a countermodel for each of the following wffs: 3x p(x) → Vx p(x) Væ (p(x, f(x)) → p(x, y))

A: Counters are an uncommon instance of limited state machines since they move straightly through their…

Q: Write a python program by following rules: Has ? discrete time intervals where ? is large.…

A: Solution:--   1)The given question has required for the solution to be provided in the form of…

Q: Show that 1. (p Aq) = vp A nq 2. ~(p → q) = p^ ~ %D

A: ~(p^q) Truth table ~p∨~q   Truth table of both are equal so they are equal

Q: Let M be an NFA with n states. Show that if |L(M)| > 1 then 3w E L(M) with w| < n. You may use…

A: In this question we have to show that if |L(M)| &gt; 1 then ∃w ∈ L (M) with |w| &lt; n. and we can…

Q: Write v as a linear combination of u and w, if possible, where u = (3, 3) and w = (2, -1). (Enter…

A: The answer to the following question

Q: the invers transform method, write an algorithm to generate a random variable from binomial…

A: It is defined as a procedure or formula for solving a problem, based on conducting a sequence of…

Q: Given the functions |logn if n even f (n) = | n³ f2(n) = min {5000 log n² , 00 } otherwise. 20000…

A: Given function of asymptotic correct or not

Q: Given the functions |logn if n even f (n) = | n³ f2(n) = min {5000 log n² , 00 } otherwise. , 20000…

A: Asymptotic notation of given function

Q: Consider the following truth table where A, B, C, and D are considered as inputs and F is the…

A: Truth table A,B,C and D to expression to solve

Q: Using the acceptance-rejection method, generate a scatter plot of N random numbers distributed…

A: ANSWER:

Q: Consider a random Telegraph signal X(t) with autocorrelation function exp(-2.4|t2-t). (a) How many…

A: Introduction to Telegraph Signal It is defined as is a noise process involving random and…

Q: Given a digraph D = (V; A; `) in which all but one arc (u; v) have non-negative lengths, describe an…

A: The above algorithm is Bellman-Ford algorithm.

Q: Show that 1. (p Aq) = vp A nq 2. ~(p → q) = p^

A: ~(p^q) Truth table ~p∨~q   Truth table of both are equal so they are equal

Q: According to the specification sheet, the average weight of the bolts is µ=30gr with o=2gr. Suppose…

A: A per guidelines we can answer only one question and for answer other questions please ask…

Q: Q1/ Let p:e N q: Thi-Qar is not in Iraq r:3 is a prime number are three propositions. Find the truth…

A:

Q: Can you change the matlab into c++ clear all; clc; %let x=t t(1)=0; h=1; Q(1)=25;…

A: Program1 #include &lt;conio.h&gt; #include &lt;math.h&gt; #include &lt;graphics.h&gt; #include…

Q: Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number…

A: Program: #include &lt;iostream&gt; using namespace std;   //definition of main function int main() {…

Q: Consider a random Telegraph signal X(t) with autocorrelation function exp(-2.4|t2-ti). (a) How many…

A: The solution for the above given question is given below:

Q: Which of following gives the correct canonical product of sums for X      A.      X = A' + B'…

A: Dear Student, As X has not been provided I am assuming it to be the case when we get 0 as output for…

Q: Provide the values of X, Y and Z such that the following FA accepts the set {All strings of 0's and…

A:

Q: Phoenix loves playing with bits — explicitly, by utilizing the bitwise tasks AND, OR, and XOR. He…

A: Here have to determine about playing with bits problem statement.

Q: Simplify the following Boolean function F, together with the don’t-care conditions d, and then…

A:

Q: For each of the following two code fragments, give its asymptotic running time in the form T(n) =…

A: Here have to determine function T(n) = (f(n)).

Q: Show that %3D 1. (p Aq) = vp A~q 2. ~(p → q) = p^ ~q

A: (1) ~(p ∧ q) ≡~p ∧ ~q This implication is wrong According to Demogorgon law  ~(p ∧ q)  ≡ ~p ∨ ~q  So…

Q: The ordinary least squares solution is given by WÖLS = (X"X) 'x"y Discuss the existence of solution…

A:

Q: e) Show that if 6 integers are chosen at random, at least two numbers will have the same remainder…

A: Solution ::  Let's see first what is pigeonhole principle? In mathematics, the (put into a…

Q: find the mean for the given data x f 1 5 2 4 3 5 4 4 5 1 6 4 7 5 8 4 9 5

A: Given data table, X f 1 5 2 4 3 5 4 4 5 1 6 4 7 5 8 4 9 5

Q: • Choose an integer r, uniformly at random from the range [1, n]. Set m equal to the remainder…

A: Here is the detailed and simplified C++ code for the above listed problem statement: