Suppose X and Y have the following joint PMF. æ\y_ 1 2 3 4 1/6 1/6 0 1 1/12 1/12 0 1/12 1/12 0 1/6 0 3 4 6 1/6 0

Q: Find the general solution of the following ODE's: y' + 3x²y = x²

A: The given differential equation is y'+3x2y=x2 It is of the form of linear differential equation…

Q: (11) Let X = n(µ,4) and Var(2x) = E(4– 7x) find u.

A:

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: Solve the following: aDx aDy aDz Əx Əx Əx if D %3D 2хya, + x?а, + ху?а,

A: D=2xyax+x2ay+xy2az

Q: x2+1 =0 Has soluion in R

A: Solution:

Q: If z + In(e 2 – e" + e*) = 0 -2x az find at the point (0, 0) O-3 O 3 O-2 O 2

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Q: Compute r for each of the following: 1. EX 225 2. EX = 32 3. EX 180 ΣΥ- 22 EY 1 105 ΣΥ-147 EX? = 9…

A: We have given that the data of X and Y in 3 sets.

Q: Find and plot the cubic spline S satisfying S(0) = 1, S(1) = 3, S(2) = 3, S(3) = 4, S(4) = 2 and…

A: %File Name: findSplineCoefficient.m %Define function function [ retCoeff ] =…

Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

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Q: - Let X1, X2, ...,Xn~N(0,0) and T = Fi (T),Var(T)

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Q: find the Solehion dy'= 4t + 2e

A: Given the differential equation :

Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: Solve the following Cauchy-Euler D.E: x²y" – xy' +y = 2x2 + In x %3D

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Q: 1- Two vecters n'and mª anl Said to be orthogenal if n'entzo T b. F a.

A: The given statement is: Two vectors n and m are said to be orthogonal if nxm=0 To determine whether…

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: FIMD dY IF x= AMD Y= U 1tu3

A: Let's find.

Q: 12) If the following is a cubic spline over [0, 2] -2x3 + 2x2 + ax + 1 , 0 <x< 1 S(x) ={7(x – 1)3 –…

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Q: Find dy ax 9=бл+бай

A: Given :y=x+1+xformula : ddxx=12x

Q: 2y edy S- e-1 y

A: We are authorized to solve only one question, please repost remaining questions Integration

Q: © If g(x, y) = In then xgx - vgw in simplified form is [c].

A: The objective is to solve partial derivative problem and explain process.

Q: (2) O show that you Y2,43, and Yu are solutians to NOTE : Geueral Solufion

A: Thanks for the question :)And your upvote will be really appreciable ;) Solution is provided below,…

Q: x²y' + 3y = x²

A:

Q: prove that var (XY) == 0} 03+ 2} · o3+ 13.03

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Q: Determine the general solution of the following Bernoulli ODE: y' + xy = x³y³

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Q: Consider the following LP Min z = 3x, + 2.x, +7x, s.t - x, + X, =10 -2x, + x, - x, <-10 *,X,,x, 2 0…

A: Hi! As per norms, we will be answering the first question. If you need an answer to others then…

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: the following DE are Bernouli type and solve: 1. y’ – x = y 2. y’ + 5y/x = x 7 y 4

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Q: Use Horner's method to evaluat P(x) = 2x – 3z? +3x -4 at xo = 2

A: Horner's method (also known as Nested scheme) uses synthetic division to evaluate the function:…

Q: 3. Vsech 2t Evaluate dt 3. coth 2t

A: Application of integration

Q: 1.1 Solve for x in cach of the following: 1.1.1 * +x-12=0 1.1.2 V2x+1 =x-1 1.1.3 2 = 27 1.1.4 x…

A: As per the guidelines we are allowed to solve one question. So please upload the other questions…

Q: 2) Show that L(1-x*)P",)P"mx) dx = 21(1+ 1) Sim 21 +1

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Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

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Q: If C + L3 = e4C, compute dC/dL when C = 0. C'(0) =

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Q: In(y) 6° Evaluate dy.

A: Consider  I=∫19ln(y)ydy

Q: a. 2,526sinx + 2,526cosx Yp 29 b. yp 89 3 M 7,930sinx + 7,753cosx 91 3 = c. Yp 3,290sinx +7,753 cosx…

A: We will find the particular integral.

Q: c). Invest diFrgate whether the given en equation is homogene eous dy 2. oxy

A: A first order differential equation is homogeneous when it can be written as a function of y/x, that…

Q: 3) yv1+x²dx + x/1+y?dy = 0 (1+v1+x²)(1+/1+y²) Ans: V1+ x² +/1+ y² In +c (Bali, 2007) xy

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Q: Q/Find af/ax and af/ay xy Iny

A: The given function is fx,y=exylny To find: ∂f∂x and ∂f∂y

Q: if y ". y (In z) (a) Find

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Q: Find the solution to the following PDES: ди y ду ди Ans. и %3D с,(ху) X дх

A: Part 1.  Given,                            x∂u∂x=y∂u∂y                  ...(1)      we have to find…

Q: that H(m m). Show

A: Given function is: Hm=3m-2 We have to find the inverse function H-1m. Let Hm=y Then we get,…

Q: Suppose A=LU. Find t, where: 1 0. 01 [2 3 4 L = 1 0. U = [0 3 1 5 3 01 0 0 1 3 0 4 and A = 1 8. 10 t…

A: given that A=LU…

Q: he joint pmf of X and Y is given below. What is E()XI-M)? Y -1 1 X 1/16 1/16 1/16 1/8 1/16 1/8 1/8…

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Q: IF Y = u²-1 u²+1 Find dy np

A: Given,  y=u2-1u2+1

Q: 2) Evaluate each of the following. Show your work. pIn(3) e2t +5 dt et a)

A: Given:        (a): ∫0ln(3)e2t+5etdt

Q: 7) Show that K± = det [ T 4 J.

A: Sol

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.