Show that 1 – R1.23 = (1 – r12²) (1 – r13,22 ) Deduce that (i) R, 23 2r,2, (ii) R? = r12² + r13², if r23 = 0 1.23

Q: 27. P (Z> z) = 0.0239 %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: pany 2 = 355 3.24 = 0.52 on about these two co

A: The null and alternative hypothesis is as follows: Given: As the population standard deviation is…

Q: Estimate the value of gqΣn=2 to ∞ (1/(n2 + 4)) to within 0.1 of itsexact value

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Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

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Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

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Q: Q5 Show that EL >². n n =1

A: Consider that x is a random variable. From the formula of population variance;

Q: Q1 (a) Calculate the coefficient of æ'yz in (r+y+2)13. (b) In her discrete math class, Karen was…

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Q: (d) For k satisfying -8 < k < k + 4 < 8, compute P(k < X < k + 4). (Round your answer to two decimal…

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Q: Evaluate the following. SP S: z = 13 - 4x + 6y, 0 Sx S 5, 0sys5

A: We have to evaluate the given double integral.

Q: Compute 5f – 7g, given that f(r) - and g(z) - e. -1) "(z-1) Se

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Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: Q3: Prove that (9":n e Z} S {3":n Ee Z} but {9":n e Z} (3":n E Z}.

A: To prove:  {9n:n∈ℤ} ⊆{3n:n∈ℤ} but {9n:n∈ℤ} ≠{3n:n∈ℤ}

Q: for n>2, 5 . Deermine for whpch n, n2-2 let |anlく,

A: Given  an = 5nn2-2

Q: 8a, 2+ 225n for n> 2 with initial conditions ao 7, a1 83 %3D

A: Given: an=-6an-1-8an-2+225n for n≥2 with initial condition a0=7, a1=83. To find: The solution of the…

Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

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Q: /2 5b) What is ll xl)=(2 ²) if x= G,s%2;X3=--) toce where -n/2 2. and Xn = L?

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Q: If z 6.57 (rounded to 2 decimal places) and y = 6.017 (rounded to %3D (a) the upper bound of x + y…

A: x= 6.57(rounded to two decimal places)  and y=6.017(rounded to 3 decimal places)

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

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Q: Find the general Selution yer r the equatiJen S/0x)-14 ()+ 0 By(x) = =D0 dlax

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Q: 2. and XR %3D C. Two tails with n = 34 , x =

A: Solution: From the given information, level of significance is 0.01 and n=34.

Q: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: 1. Differentiate the following with respect to x: a. y= 5x - + 5Vx + 3p ex + In(x) - 7 (9)

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Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: q² – 1 19. Find if p= In dą

A: By means of calculating derivative of any function of a real variable we measure the…

Q: Suppose f"(x) = N,(h) + a,h + azh³ + azh5 + .. The value of N2(h) using Richardson's extrapolation…

A: The value of N2(h) using Richardson's extrapolation is: N2 (h)=2N1 (h/2)-N1 (h) with error of order…

Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: convcrges for all r. n! n=1 Σ 24. Show that

A: To show the series∑n=1∞rnn! is convergent for all r; ratio test can be used. Ratio test rules that…

Q: The vahue of f(1.7) from the following table by using Gauss interpolating formula is *012| 3 4 f) -2…

A: formula for gauss forward interpolation is q=x-x0h…

Q: n! Verify that Ex1+…+xr=n,xi20 r^n for any r, n>1 x1!x2!...xr!

A: Consider the given information. Let n is greater than equal to 1 arbitrary. Use the mathematical…

Q: a2 z a2z If z = In(x² + y²), find + 2 Əx2 ду?

A: The given function is z=ln(x2+y2).

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Employ a suitable c 2n² +3n diverge (a) V5+n² n=1

A: ∑n=1∞2n2+3n5+n5limn→∞an+1an= limn→∞2(n+1)2+3(n+1)5+(n+1)52n2+3n5+n5= limn→∞…

Q: Describe the long run behavior of f(n) = 3n – 4n³ – 5n° + 5 As n → - 0, f(n) → ? As n → o, f(n) → ?

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Q: d. What happens if P < M for all t?

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Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

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Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: (b) Verify that 17(s +1) (s² – 2s – 3)(s2+2s +2) s+5 (s – 3) (s2 +2s +2)

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Q: 3 Reverse the order of whyndien of ? X (6x-2) dyds x- 4

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Q: Let f (x) = -2r, de fined on -1, 1], then L (P ) = 2 (n– 1) 2- 4 (n+1) 4 (n – 1) 4 (п-1) 2n2

A: We need to find the lower Riemann sum

Q: Q2) compute the missing values of yn and Ayn in the following table: yn Ayn Yn4² T -0.39

A: Introduction: Interpolation is the process of estimating the value of a function for any…

Q: Q2: A: IF B = By using the result of det(A) (JA) Find the value of det(B) ([B]) without use the def…

A: Given :A=123456101

Q: Q2) let A = [ 1 find e4t using Gauss-Jordan method.

A: First we will find the eigenvalues and corresponding even vectors of the matrix by Gauss-jordan…

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

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Q: Suppose that X ~ Unif(-1,1). Compute (d) P(X = 0.5), (e) P(X² > 0.5).

A: Let ,  The pdf of X is ,  = 0 ; otherwise Our aim is to find the following :  d) P(X=0.5) e)…

Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

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