(a) A definition which captures the idea of a process getting stuck somewhere for ever. (b) A result which involves ignoring certain arrivals in a Poisson process. (c) A definition of a method of representing a Markov chain in a way that allows linear algebraic methods to be applied.

Q: Proof of SAS Congruence Theorem.

A: I am attaching image so that you understand each and every step.

Q: Give an inductive proof of the following identity where Fn is the math Fibonacci number F0^2 + F1^2…

A: To prove  f02+f12+f22+...+fn2=fnfn+1          1 where fn is the Fibonacci number

Q: Prove that if B (is included in) A, THEN P(B) < P(A)

A: Given :  Set B is included in set A To Prove : P(B) &lt; P(A)

Q: Part II Write the first five B={ IneN3 then prove sup(B) = l Part III Proue that Pj ajta and b,sb →…

A: a) Supremum of set: Let  S be any subset of real numbers. Smallest upper bound among all upper…

Q: 1 For any integer k, 3|(2k² + 1) if and only if 3 k

A:

Q: Determine all s ER such that i" - (i*)".

A: We have to determine all s∈ℝ such that ι4s=ι4s, where ι denotes the iota in a complex number. We…

Q: Let A be a set with |A| = n. Using induction, prove that |P(A)| = 2^n .

A: To show that the cardinality of power set of A is 2n when given that cardinality of A is n.

Q: Consider the following families of sets indexed by the set of natural numbers. Which among these is…

A: Given: Intersection or union of a family of sets. To find: Which of the intersection or union of a…

Q: Prove Tietze extension theorem in your own language

A: Tietze Extension Theorem states that "Let X be a normal space, let A ⊆ X be a closed subspace,and…

Q: If sup(S) exists, then it is unique ylgn ihi

A: The solution is given as

Q: we have the following WFF of the quantificational calculus: ƎxƎy∀z (p(z) ∧ q(x,y) (r(w) ∧ ∀w…

A: Given: The following WFF of the quantificational calculus: ∃x∃y∀zpz∧qx,y↔rw∧∀wSw,y   To determine:…

Q: Explain the Wronskian Derivation?

A:

Q: Find all integrs n Such that

A: We have to find all integers 'n' such that ϕ(n)=n3ϕ(n) is a Euler totient function which means ϕ(n)…

Q: Let f= (14723 5 6) and g = (1 5 3 264) be permutations in S. What is the second line of fin two-line…

A: Introduction: Permutation businesses are mathematical businesses whose individuals are permutations…

Q: hat meaninig in abstract algebra that under isomorphism units maps to units

A: Suppose f is function that maps from units  to units. The given f is isomorphic.

Q: A drug using to treat a particular disease shows 20% failure rate. If we select a sample of 8…

A:

Q: Prove the identity 1+z+z²+...+z"-1 th if = 1-z" 1-z on th noot of: 2 for z 1. ait other than 1 +

A:

Q: Give a recursive definition with initial conditions of the set S SEE IMAGE

A:

Q: find fundamental set of soleubions cwith d real va lues for

A: Using differential equations,

Q: 1 5) Show that 7. diverges. + + + +

A: In this question we have to prove the series is diverges.

Q: Give an example of a closed subset S of R^2 such that conv S is not closed

A: An example of a closed subset S of R2 such that conv S is not closed is given below.

Q: What is Fn * Fn+1 with F representing Fibonacci numbers

A: The objective is to find Fn×Fn+1 where F represent Fibonacci numbers

Q: Prove that If P(A) > P(B), then P(A/B) > P(BIA)

A: The conditional probability is defined as P(A | B) = P(A and B)/P(B),  P(B | A) = P(A and B)/P(A)

Q: What is proof of Neyman-Person Lemman Theorem ?

A: Neyman-Pearson lemma theorem basically helps us to find the best critical region. Statement: let X1,…

Q: whether the selic) H6 use un appropriate test to determine whether the" selics gilon wnverges or be…

A:

Q: Consider the following families of sets indexed by the set of natural numbers. Which among these is…

A:

Q: What is the maximum number of people you can invite so that at most 3 guests are born same month?…

A: The Pigeonhole Principle: If n + 1 objects are placed into n boxes, then some box contains at least…

Q: one of themore important theroman real ani llyGes is Fa tou's lemma. state the lemma and say…

A: In the question , basically asking for Fatou's Lemma and its proof .   Fatou's  Lemma  :  Let {fn}…

Q: prove the following combinatorial identity  P(n,k) * (n-kCm-k) = (nCm) * P(m,k)

A: p(n,k)=n!/(n-k)!

Q: Question 4 x- X + 3. what is the foge coveryer of the power serres? a) -d <xet b) -1<x1 c) d<x<

A:

Q: Define dircect proof

A: Direct proof: a direct proof is a way of showing the truth or falsity of a given statement by a…

Q: Consider the set L:= {(a,b) E Z²| (a – b) is a multiple of 3}. A proposed recursive definition for L…

A: Consider the provided question. L=a,b∈L'a-b is multiple of 3 therefore, a-b=3ka=b+3k  where k is an…

Q: People with high blood pressure suffer from hypertension. Data on fasting blood sugar…

A: Given: Data on fasting blood sugar (milligrams/decilitre) and magnesium (milligrams/decilitre) in…