Laguerre's differential equation xy" + (1-x)y'+ ny = 0, n = 0, 1, 2, ..., has polynomial solutions L(x). Put the equation in self-adjoint form. y]+[ )y=0 Give an orthogonality relation. For m = n, m(x)Ln(x) dx = 0.

Q: If A × B ={(p, q),(p, r), (m, q), (m, r)},     find A and B.

A: A will be the set of the first ordinates  And B is the set of the second ordinates

Q: 3. It has to: i = (2, –3,4); i = (-5,1,0); w = (4,2,1), perform the following operations: u+v; u-w,…

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Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

Q: Write what is Cohen’s Guidelines for d?

A: The formula for Cohen's d value is obtained below:

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A:

Q: Under what conditions on u and v is II u + vII m = llull m + llvll m? Explain your answer.

A:

Q: Find the mean of the regression squares X y 14 7 11 9 13 10 23 11 56 12

A: Given: Sr. No. x y 1 14 7 2 11 9 3 13 10 4 23 11 5 56 12

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A: option e is correct see below the explanation

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Q: 3+2i Evaluate 4-i

A: The given complex number is 3+2i4-i. The conjugate of the denominator is 4+i.

Q: 2 0.05 0.14 0.32 (a) What is P(X = 1 and Y = 1)? P(X= 1 and Y= 1) = (b) Compute P(X ≤ 1 and Ys 1).…

A: We have given that Joint probability distribution function of X and Y.

Q: C. Show that both R and R² may be covered by countably many open balls.

A: Firstly we have shown that R may be covered by countably many open balls. Let us  consider the set…

Q: sinz = 0 iff %3D Select one: O z= kt. Oz=-+2kn. TO O z = + kt. 3T + kT. 2

A:

Q: If A and B are independent, and the P(A) = 0.35 and P(B) = 0.45 find: a) P(A ∩ B)…

A: Given that P(A) = 0.35 P(B) = 0.45 A, B are independent events.

Q: 200 398 1059 202 399 808 331 660 1228 169 318 199 247 490 261 230 485 172

A: Expt  A B C AB AC BC ABC 1 1 - - + + + - a 2 - - - - + + b 3 + - - + - + ab 4 + - +…

Q: If u = (3,0), v = (1,2), and w = (1, –1), find a and b such that u= av + bw b = (enter numerical…

A:

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: Given that v = ⟨0, –2⟩ and w = ⟨5, –8⟩, what is w – v?

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Q: 1= z In zdz

A: Given, ∫ xlnxdx

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A: Kurtosis is one of the measure of dispersion under the central tendency.  This give an idea of the…

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A:

Q: Let U{m,n,o,p.q.r,s,t,u,v} and K{k.l.m.n.v). Find the compliment of K (K').

A: We have to write the elements of U which are not in K

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Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: If delta is large according to Cohen's classificantion, then the difference between u1 and u0 is…

A: Given that - If delta is large according to Cohen's classificantion, then the difference between u1…

Q: Compute the SVD of QA = 3 2 3 322

A:

Q: L [1\ucos Puf) Ju

A: 1st we will find value of integral using integration by parts and then use Laplace transformation…

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Q: Let U = {x | x is the name of one of the months in a year} J = {x | x  U and x begins with the…

A: Given that U = {x | x is the name of one of the months in a year} J = {x | x U and x begins with the…

Q: Prove: For allintegers aandb, if a|b then a² |b²

A: