Prove the uniqueness of the Poisson equation with Robin boundary condition DE: - Au = s, in 2, BC: Vu n+ au = 0, on an, where f is a given source term, n is the outer normal direction, and a > 0 is a positive constant.

Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

A:

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

A: Given,

Q: d) Find the asymptotic distribution for the parameter h(B) = e® assuming that a is known. 0, e2B B…

A:

Q: Suppose that a continuous function g satisfies: 3 g(x)dx = 6 and | 9(27)dz = 9. 0, | z9(3z*)dz. Find…

A:

Q: Let X1, X2, ...,X, be a R.S of size n that have the pdf f(x; B) By using method of moment find the…

A: Given information: Let X1, X2, …, Xn is a random sample of size n taken from a probability…

Q: Let f(=) = In[=*(z +8)*(z² + 8)°] f'(z) %3D

A: Given that fx=lnx3x+85x2+82 To find f'x

Q: What does it mean to say that the real-valued RVs X and Y are inde- pendent, and how, in terms of…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Zt +0Zt-1, t = 1,2,..., where Zt~ IID(0, 2). Show that Xt is both weakly and strictly Let Xt =…

A: To show that a process is weakly stationary, we need to show that its mean and autocovariance…

Q: a) Consider the utility function of Carin where: (i) 1/2 U (9₁, 92) = 3 × 9₁ 1/3 x 92 91 = total…

A: Here we have to find marginal utilities of product 1 and 2

Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

A:

Q: A curve passes through point leio) and the Sloge dt line of each point (^,y) is egual to xe-BY .In…

A: Curve passes through (e6, 0)f(e6)=0slope of Normal line=x e-8ySlope of normal line*slope of tangent…

Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

A:

Q: i) Assume a MA(1)-process given by Y = c+ e +6ɛ,-1, E, ~ N(0, o?), t= 1,... ,T. Compute the…

A: A time series is a sequence of observations taken sequentially in time.

Q: A normal is drawn at a point P(x, y)of a curve.lt meets the X axis and Y- axis in the points A and…

A:

Q: Page 142, 2.6.1.* Let X, Y, Z have joint pdf f(x, y, z) = 2(x + y + z)/3, 0<x< 1, 0<y< 1,0 <z< 1,…

A:

Q: Q1\ A) Find average value over the given interval [1, 3] : F(x) = Vx + 4

A:

Q: If X has a normal distrbution with parameter u and o² then we write x ~N(0,1) ylgn ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: ) Find MThe equation of The normal to 5 at the point (a, 4) y=dx

A: Given curve is x2+y2=5. To find the equation of normal at the point (2,1). Solution: Given curve is…

Q: A) Given the following function and error margins of each variable, compute the propagated error for…

A: Given, The function f(x,y,z) = x2y3+1z The uncertainty is defined as x=2±0.03, y=5±0.4, z=3±0.1   We…

Q: With n=15 and p=0.4 Find: a) P (X to be between 3 and 5) b) P(X at most 7) Prove the use of normal…

A: We have given that  n=15, p=0.4.

Q: Find o r(t)dt if r(t) = (cos t, sin t, 3t²). %3D O A.O B. (0, 2, ³) OC (0,0, x³) O D. (0, 2, 7) O E.…

A: We have to choose the correct answer from the given option

Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

A:

Q: Find the PDF M = X + Y when X and Y have the joint PDF: f_X,Y(x,y) = 2 for 0 <= x <=1, 0 <=y<=1 and…

A:

Q: CALCULATE C , 1) dt.

A: Topic - integration

Q: Evaluate the path integral SF. dr, where F(x, y) = yi + xj and C is the line segment from (0, 0) to…

A: The given problem is to evaluate the given path integral of the vector field in the given path of…

Q: (p;-q,)? 2. Prove that KLD(p||q) = J6 t Eisisn pitt(ai-p) dt. %3D

A: Given: To show the given statement as follows: KLD (p|| q) = ∫01t ∑1 ≤i ≤ n pi-qi2pi+i( qi- pi) dt

Q: Q2. In the bank example in page 44-45 of the slides, the joint pdf of X, Y i given by 6 fxx(x, y)…

A: a) The marginal pdf is calculated as follows: fy=∫xfx,ydx=∫0165x+y2dx=65x22+y2x01=6512+y2…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.