Give a recursive definition for the set of all binary palindromes, that only '0's and 'l's that are the same forward and backward. Hints: What are the

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1 =…

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Q: A student claims that he does not need to define permuta- tions because he knows the Fundamental…

A: A permutation is the arrangement of objects where the order of arrangement is considered. The…

Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: if b is modulo m and a is another unit with a=b mod m, we say that d is the---------of a modulo m to…

A: As with such a large amount of concepts we are going to see, congruence is straightforward, perhaps…

Q: 6. List all the numbers a such that you can find an a such that ax = 1 modulo 26? call such…

A: 6. For a particular n, all integers which are less than n and co-prime to n, will be invertible…

Q: +3 + 32 +.+3" 2 = 4"

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Q: What does the K stand for in Kn? (Finite)

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Q: Give a recursive definition for the set S ={4,7,10,13,16,19,.}.

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Q: QUESTION 1 How many binary strings of length 24 have exactly 17 zeros?

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Q: Suppose a, n E Z and 0 < a<n. Prove that )-(".")-(C ) n- 1 in = a a а — 1 in two different ways:…

A: We have to prove, na = n-1a+n-1a-1 First let us prove this using formula. Using Formula…

Q: The distinct characteristic roots corresponding to the recurrence relation an=7an-1 -10an-2 are:…

A: Substitute the value of , we get

Q: Suppose we have a Boolean formula with 4 input variables. When we draw the Karnaugh map, there are 6…

A: In 2×1 or 1×2, only one literal changes is value. Therefore we have one less literal in each terms.

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

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Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: Prove that if we move straight down in Pascal's triangle (visiting every other row), that the…

A: In any Pascals triangle nk, n≥k≥0 When we move 2 rows down and move 1 over then it becomes n+2k+1 we…

Q: Find the smallest positive integer n, пп such that 0 and 0 are 2 coterminal. And give an example

A: Coterminal angles are the angles in the standard position having a common terminal sides.

Q: Suppose that residue(modp) 8) Let odd prime P. atzis Show that has be an not Diophantine…

A: Given that a is not a quadratic residue mod p. That is there does not exists an integer z such that,…

Q: Consider the pseudorandom number generator given in our lessons: with Uf +1 = (auf + b) mod m…

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Q: SHOW THE FULL SOLUTION OF THIS PERMUTATION 3!

A: Given3!

Q: Table below show the heights of the 5 starter players of 5 basketball teams in a competition. Every…

A: Introduction: Different teams may use different measures to determine whether they are the tallest…

Q: The number of substrings (of all lengths inclusive) that can be formed from a character string of…

A: A string is a set of characters. A substring is a set of characters that can be formed by taking 1…

Q: or an integer n>=3, an n-gon is an n-sided polygon. (example, a 3-gon is a triangle, 4-gon is a…

A: To prove: the sum of the interior anles of every polygon with n sides is n-2180° Now we shall take a…

Q: 1. Show that an integer n is divisible by 2 if and only if its last digit is even. (Hint: For each i…

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Q: Find the inverse of 35 under mod 233(if exixts), by using Euclid's Algorithm?

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Q: Let S be the set of bit strings defined recursively by λ ∈ S and 0x ∈ S, x1 ∈ S if x ∈ S, where λ is…

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Q: Use the Generalized Euclid’s Lemma to establishthe uniqueness portion of the Fundamental Theorem of…

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Q: Show that the Post Correspondence Problem is decidable over the unary alphabet S = {1}.

A: To Prove :- The Post Correspondence Problem is decidable over the unary alphabet S =1.

Q: Consider the following claim: Claim: It is possible to find a bit-string with 34 binary digits, such…

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Q: Let S, be the set of strings, formed by the alphabets {h, k}, of length n and with two consecutive…

A: Let Sn be the set of rings, formed by the alphabets {h,k}, of length n and with two consecutive h's…

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator r1= (4r,…

A:

Q: Theorem 24. If ɛ > 0, then there is an integer N EN such that 0 < + < e. .

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Q: Suppose that lal = 12. The number of distinct left cosets of in is: * %3D 12 O 10 O None of the…

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Q: 2. The binary operation * defined on Z by x * y = 1 + x + y on the set of real numbers. Show that *…

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Q: Find the first five terms of the séquence an= 1 as as express in Standard form

A: Given  an = 1+ 1/n  To find the first five terms

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

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Q: When we work with a congruence class, we have to keep two key things in mind. First, we have to know…

A: For ℤ3, The ones that are congruent to 0 is the set {...,-6,-3,0,3,6,..}. We call it the congruence…

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters co can be generated?…

A: Given: There are 7 letters A, B, C, D, E, F, G

Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Q: Show that the set of a+bi Gaussian integers has the same strength as the set of natural numbers N.

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Q: ocedure can be broken down into n tasks, where each I task can be performed ti Prove via induction…

A: Given: To prove that the procedure Pn can be performed t1, t2, t3 … tn ways.

Q: With reference to Exercise 1, suppose that there is athird step, and if the first step is made in…

A:

Q: Prove by CVI that every natural number n > 2 is a product of prime numbers. NOTE. A prime number p…

A: Every integer greater than 1 can be written as the product of prime numbers. In other words, every…

Q: Let x, y, N E N be n-bit integers such that N > 2. . If x < N, the value x" mod N can be computed…

A:

Q: Find the integer a, if the modular representation of a is (2, 1, 5) with respect to the modulo 3,…

A: We have to find the integer a if the modular representation of a is 2,1,5 with respect to modulo 3,…

Q: Provide a combinatorial proof that includes quarternary strings {0,1,2,3} to prove that: (:) - () +…

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Q: ences have the following generating

A: We have to choose the correct options from the given options according to the given information

Q: If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which…

A: As we know that any truples h,i,j,k,m with n≥h≥i≥j≥k≥m≥1  can be represented as a string of n-1…

Q: -show that. Z, ax Rings.

A:

Q: How many times will the innermost loop be iterated when the algorithm segment is implemented and…

A: 1) i greater equal to (&gt;=) j  2) j greater equal to (&gt;=) k  3) k greater equal to (&gt;=) 1.…

Q: Suppose that you start browsing the internet on a specified page c. Let x be all the websites you…

A: The process in which a function calls itself directly or indirectly is called recursion and the…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!