6. Given the following sequenvces in R: {yn}1 = {(-1;1); (1; – 1);(-1;1);(1; –1)·.} 27 (a) Write out the nth vector of each sequence. (b) By referring to the properties of sequences in multiple dimensions, either evaluate the following or state why you cannot. i. limnXn + limn→∞Yn ii. limn+05x, – limnZn

Q: Find lim,00 sup(sn) and lim,→0 inf(sn) for the sequence: 82n = (-1)"(n); s2n-1= e7 = et

A: The sequence is S2n=-1nn. Find limn→∞sups2n and limn→∞infs2n: Consider and obtain the limits:…

Q: | 0 0 1 1 1 00011 0 0 0 0 1 5 (If the arithmetic for computing an entry involves huge powers, you…

A: As per bartleby guidelines we are allowed to do maximum of 3 subparts

Q: Find the order of: (c) (Z/100Z)*

A: We will use the fact that U(n) is isomorphic to (z/nz)^× to find order .

Q: Define the sequence of functions {fn(x)} on [0, 1] by { 2n2x; 2n(1 — пх); 0; fn(x) = 2n 1 n (a)…

A: Given: fn(x)=2n2x;            x≤12n2n(1-nx);    12n<x ≤1n0;              1n<x, x∈[0, 1].

Q: Which of the following is the generating function for the sequence 5, 5, 5, 5 O A. G(x)=(1-x) 1 O B.…

A: Generating Function: Generating Function is a way to represent an infinite sequence. Consider a…

Q: Determine the generating function for the following sequence: (),-), (2),,(-1)" (a),.. where a is a…

A:

Q: 22: Establish the divergence of the sequence x, =(-1)"

A:

Q: a,=(- 1)" is a divergent sequence

A:

Q: Show the function f1(x) is primitive recursive. f1(x) returns n if factorial(n) = x but returns 0 if…

A:

Q: Let x be the number of teachers among 3 people selected randomly from a group  consisting of 3…

A: Probability: Probability is the ratio of favourable outcomes to all other potential outcomes of an…

Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

A:

Q: Consider the quadratic function : C→C defined by f(3) = ² + i. (a) What is the long term behavior…

A: Given : A quadratic equation f:ℂ→ℂ defined by f(z)=z2+i. To find : (a) The long term behavior for…

Q: For the sequence {a ,} if a,→ L, and f(x) is a function defined at all a, then f(a ,)→ f(L) Select…

A:

Q: 5. (i) Determine the sequence gnerated by the following generating functions: (ii) e(1+x) t (1-1)³

A: (5) (i)          Given generating function is t1-t3= t 1-t-3…

Q: Give combinatorial proofs of the following identities. (a) {"} = 2"-1 – 1. (b) {„",} = (3). (c)…

A: Given: Let us show the combinatorial proofs of the following identities a) n2=2n-1-1 b) nn-1=n2 c)…

Q: What is the relations (5)/(8) and (8)/(10) Drag and drop a tern

A: Ok

Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

A:

Q: numerically greatest

A:

Q: For the model (1-B)(1-0.2B)X(1-0.5B)a,, find forecasts for one and two steps ahead, nd show that a…

A: Given: Let Xt∧k=1.2 Xt∧k-1-0.2X∧tk-2 ---(1)

Q: Show that (an) is increasing

A:

Q: Justify each step in the following proof sequence of (Ax)P(x) ^ (Vx)(P(x) → Q(x)) → Ax)Q(x) 1.…

A: Given: ∃xPx∧∀xPx→Qx→∃xQx. We have to justify the steps of the proof: 1. ∃xPx 2. ∀xPx→Qx 3. Pa 4.…

Q: Find the sequence for the generating functionG (x) = (1-x) 1-x

A:

Q: Find explicit formulas for sequences of the form a1, a2, a3, . . . with the initial terms given…

A: Given that the sequenceAnd  To find the nth terms

Q: Find the first three terms of the sequence (B₁f) of Bernstein polynomials for f(x) = x³.

A: The sequence of Bernstein polynomials for a function f(x) is defined as follows:B_n^k(x) = C(n, k) *…

Q: (b) Consider the set U = {(x, y) E R² : 2x + y < 1, x 2 0, y 2 0} and let Zn = (Xn, yn), where Xn =…

A: NOTE:- I HAVE REQUIRED QUESTION A TO SOLVE QUESTION C AND D. THEREFORE I AM SOLVING ONLY QUESTION B.

Q: Find the inverse z-Transform 2z 3z X(z) Z-1 == Z + e-4 of the sequence defined by: 15z (z - 5)²

A: Given Information:To find:The inverse  transform of the given sequence.Concept used:If  is a pole of…

Q: If lim(x,) =5100, then (Xn) is bounded. Select one: O True O False

A: 1) Here, lim (xn)=5100 that is finite. That is the sequence xn is bounded. So, the statement is…

Q: Evaluate х3 (x* — 1)3 dx x*(x* – 1)ª + C (x* – 1)* + C 16 4x4 (x* – 1)4 (x4 – 1)4 + C 16 + C 4

A: The given integral is; Integration of x3(x4-1)3.

Q: Given the machine number 1 10101010101 101010101 then the decimal equivalent to this number is:…

A:

Q: (-1)" :n Determine if A is bounded above, bounded 2. Let A = n below, or both. If it is bounded…

A: Bounded above. Bounded below.

Q: (prore) using sequences とす、

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.