Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

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A: The appropriate Null and Alternative Hypotheses are given below:   Null hypothesis:   H0: µ1=µ2.…

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Q: 6. Use an appropiate linear approximation to estimate the value of In(1.01). Compare your…

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Q: Assume that your computer completes a 5000 equation back substitution in 0.005 seconds. Use the…

A: Given: The computer completes a 5000 equation back substitution in 0.005 seconds.

Q: What happens in Newton’s Method if your initial guess happens to be a local min or max of f ?

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Q: how do you find z sub alpha over 2 using table a-2

A: I am solving this question by taking an example Let us take α = 0.05 We need to find

Q: 5Find the Orthogonal trajectories of the family of r=aeº

A: Question:- Find the orthogorial trajectories of the family of r=aeθ ?Solution :- We have r=aeθ -(i)…

Q: Section 3.4-The product rule and Quốtiént rule In(x) Differentiate: Y dy Preview %3D dx

A: Given: y=ln(x)x9

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

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Q: 13.3.9 Evaluate -x)-Pdx a beta function. as

A: Use the property of beta function to evaluate this integral.

Q: the Following is divergent

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Q: 3. Find an orthonormal pair one of whose members is proportional to (4, -3).

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Q: a mortality study of insurance applicants in two countries, you are given: Country B d, Country A d,…

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Q: Find the Hessian of the function. Based on result in c), determine the types of stationary points…

A: We need to find the Hessian and stationary points of the function f(x,y)= x3+y2-2xy.

Q: .Prove that e- -dt < (1+ t²)* 1/4 6.

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Q: Let X1,..., Xn be iid pdf (log(æ)-®1)² 262 1 f(x) -00 < x < o0, and unknown parameters 01 and 02.…

A: Let X1,X2, X3...be iid with pdf, f(x)=1x2πθ2e-(log(x)-θ1)22 θ2          -∞&lt;x&lt;∞   The…

Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Calculate the average power value of X (n) =5cos(n. π /6) + 6 as defined in discrete time??  I would…

A: This question is about application of powers in signals

Q: consider che funceion h= w²-8.Tawei Determine dh/dt and w= St"-26

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Q: How do i find e(x), var(x) and e(x^3) using the moment generating function

A: Let us define the random variable X with moment generating function Mx(t).The moment generating…

Q: 1. Use a linear approximation to estimate the given number. е0.1

A: We can use linear approximation in order to solve the given problem.

Q: Find an upper bound for the Lagrange interpolation error for f(x) sinh(x)+2 cosh(x) over the…

A: Given: fx=sinhx+2coshx, x∈0,2. Interpolation nodes xk=k4, k=0,1,⋯,8. To find:          An upper…

Q: x cos 5x dx Ste-* dt -3r

A: Solution of above question is written below.

Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: How to find and identify all singular points of legendre's equation of order n?

A: A differential Equation P(x)y''+Q(x)y'+R(x)y=0 can be written as y''+Q(x)P(x)y'+R(x)P(x)y=0 x=a is…

Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: Assume that after w months, butterflies’ populace in 1000 is calculated as: f(w)=12w+cos⁡(16w)+n×100…

A: Given: Butterflies’ populace after w months is given by f(w)=12w+cos⁡(16w)+n×100 in 1000 where n=824

Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

A: To determine c such that f© is equal to the average value of f(x).

Q: Number 8

A: first find the derivative.

Q: Prove that the arc y = log secx from les (2+ 3

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Q: Briefly discuss the origin/history of De Moivre's Theorem.

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Q: Example 8.19. Use Romberg's method to compute dx 1 + x² correct to 4 decimal places.

A: Let y = 11+x2  and let I = ∫01dx1+x2take h = 0.5 =12The tabulated values of y are   x0 x1 x2 x…

Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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Q: An RL circuit has an emf of 5 V, a resistance of 50 Q, an inductance of 1 H, and no initial current.…

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Q: Estimate the In (1.1) and sec (0.1) Using a linear approximation and without using any kind of…

A: f(x)=ln(x) f'(x)=1/x f(1)=ln(1)=0 f'(1)=1/1=1 linear approximation is then L(x)=f(a)+(x-a)f'(a)…

Q: 5- Suppose X, and X2 are i.id observations from the pdf fa,ß (x) = axa-1e-x" ,x>0, a > 0 Show that…

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Q: 1. Find the optium path for f=xy³ from (2,1,2)

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Q: Consider that two students (Student A and Student B) are working on a joint project. Each student…

A: Effort Level is given by ei=0,1,2 for i=A,B Denote Emin.=min.eA,eB   Grading Scale is given by :…

Q: 1 Use either (3) or (8) in Section 8.6 to find upper bounds for the error in approximating dx by the…

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Q: What does Peano's  EU Theorem 6.1 guarantee for the IVP dy/dt = -t/y,  IC(t_o, 0)

A: Peano's theorem: Let f: Dom f→Rn be defined in a neighborhood of (t0, y0). Consider the initial…

Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

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Q: Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as…

A: Consider the given function. fx=xn The Gini index is defined as, GI=2∫abx-fxdx

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.