Verify that Al2 = I½A = A for an arbitrary A E M2x2(C).

Q: by first- shifting find L(t2 e-3«) = %3D (s+3): ; * 0 a O (s+3) 2 * b O 3.cO (s+3) 3 1

A: Solution:- Correct option :- a Detailed explanation

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

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Q: For which values of a does x + a = 0 have a solu­tion in Z5?

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Q: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

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

Q: tes, sno W inut E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 and

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Q: Find the general solution to the following ODE: dy dr - 6zy + z*y

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Q: If e dy then y-

A: We will evaluate the following Integral.

Q: For ey – In x=y2, find the value of k so that (y'-y"')=1 at y=0- e O 1 O e

A: Solve by double differentiation

Q: For a non-negative integer n20, J,=| (In.x)" dx. Express J, in terms of J„- for n21. Hence, find J,.

A:

Q: (a) It is possible to have E(XY)=E(X)E(Y) when X and Y are not independent.

A: We know that if the Karl Pearson correlation theory, If X & Y are independent then we say that…

Q: s evaluate e of 1. The

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Q: If E(X") = (r + 1)! 2", then, the moment generating function Mx(t ) = E(eXt) is (1-2t)2 False True O

A: If we Calculate first moment by using both the expression. It should be same otherwise it is false.

Q: If fit) = e-lt|, then (dx/1 + x2) =.. 2 2n

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Q: Let a be a constant. Given that 3? In(ax)dx = e1² ( 12 3 -23 find In a. 3

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Q: Find a general formula for dr ax + b dx" cx +d

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Q: Solve The Following Formula For T. U=M+Mrt t=_____

A: The equation is given by U = M+Mrt To evaluate : An expression for t

Q: e2 In x dx e

A: We have to calculate the definite integral  By using substitution method  Putting  lnx = t…

Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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Q: Evaluate the following integral e-24 8(t – 1)dt A) e-2 B) e² C) e-1 D) E) 0 e

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Q: Sor's Evaluate e" 2e* 5e dx

A: The given integral is ∫ex2ex5ex dx

Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

A: Please see the below pictures for detailed solution.

Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

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Q: Find the general solution to the Bernoulli-type ODE x²y' + 2xy = y°, for x > 0.

A: Bernoulli's equation is a special type of first-order linear ordinary differential equation. When…

Q: 1 Q4) If vZA =, such that AA" = I. Find x?

A: Transpose of matrix

Q: Work out the following | (2x + 1)e² -z da =

A: we use substitution method to solve this integration

Q: A- Find the integrating factor of the following D.E 2

A: a) Here we have to find the integrating factor of given differential equation:-  We have,  Compare…

Q: Find z when In z = e – nj

A: Complex number

Q: Assume the model: Y = 5 - 2X + e , where e ~ N(0,81) What is the Pr(Y>10) when X =2? And What is…

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Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: The linear approximation of e is O a. 1.1e O b. 1.1 Oc.e Od.0.1e

A: Linear approximation of e1.1 e1.1=e1+0.1=e1*e0.1=e*e0.1

Q: Find the G.S. about xo = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0 ||

A: Given DE is  (x2+4)y"+2xy'-12y=0 Given point x0=0 is an ordinary point.

Q: Suppose E(X) = 4 and E[X(X – 1)] = 25.5. (a) What is E(x2)? [Hint: First verify that E[X(X – 1)] =…

A: Given: EX=4EXX-1=25.5 So, a) EX2-X=25.5EX2-EX=25.5EX2=25.5+4=29.5

Q: 6. 81n V81 - 81 – x²dx 4 A. Show that B. Use (A) to evaluate In 4 (e2x – e*) /81 – (e* – 1)* dx. - -

A:

Q: Let z=xln(x2+y2-e4)-161xy, x=te, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be“, then…

A: From the chain rule, ∂z∂t=∂z∂x×∂x∂t+∂z∂y×∂y∂t Now,…

Q: Calculate the residue of e.e5=0

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Q: Find if y = [In(e* + 1) + ešin #]³. Do not simplify.

A:

Q: Calculate E(X³), where X has the following PMF: .5 x=1 f(x)=.3 x=2 2 x=3

A: Given that  PMF of X is  x 1 2 3 f( x ) 0.5 0.3 0.2

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: 47. Let the assumed particular solution for the given DE be yp = (Ar + Bx² + Cx)e + E. What is the…

A:

Q: *find te general Souliton hor the XZP +YZq =XM

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Q: N 25 )X= 125 SX2 = 650 EY2 = 460 EXY = 508 t was, however, later on discovered at the time of…

A: Given: N=25 ∑X = 125, ∑Y= 100 ∑X2=650 ∑Y2=460 ∑XY=508 Two pairs are taken as (6, 14) and (8,6)…

Q: If we know that E (") (x" 1) = ("†").t then show that Eo (") -C") r3D0

A: Given information: The given theorem is:

Q: Find The coefficient cof x ard X in The expasion of Ox°-)

A: We have to find the coefficient of x9 and x10 in the expansion of given series.   According to our…

Q: If X x2(m, mµ²) find the corresponding (a) mgf; and (b) characteristic function.

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Q: S)dt =, then f(2) - If (A) 32 (B) 0 (C) (D) (E) 5 (F) None of the above O A OD OF B O E • in -

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Q: e: ZN ZP

A: Given: MN¯≅MP¯, NO¯≅PO¯ To prove: ∠N≅∠P

Q: e obtained by r

A:

Q: = 11% and E = 715, calculate the Еxample 4: If К. stock value of XYZ Ltd. for: 2) r= 11%

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Q: de Evaluate z(ln z)" Lütfen birini seçin: b.00 c.1 O'P d.0 e.-1

A:

Q: find the general for al soluh'an 3yC3) (e)

A: The given differential equation, y(4)+3y(3)+3y(2)+y'=0