Determine if the binary quadratic form is equivalent to over
Find the discriminant for the 2 binary quadratics and compare them.
Determine if the binary quadratic form is equivalent to over 5.2 + 26.0y +5941 26.x2 +...
Quantum mechanics. A Hamiltonian of the form , is equivalent to the Hamiltonian of a harmonic oscillator with its equilibrium point displaced where and C are constant, find them. With the previous result, find the exact spectrum of H. Calculate the same spectrum using the theory of disturbances to second order with . Compare your results. Calculate the wave functions up to first order using as a perturbation. P2 22 P2 Tm We were unable to transcribe this imageWe were...
For each compound: 1. Determine the number of equivalent hydrogens - number of different signals 2. Determine the splitting pattern of each signal 3. Sketch a possible spectrum 4. Then try to match the compound to the correct NMR spectrum er w t & You We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageNMR worksheet H-1 (proton NMR D for each compound 1. Debamia the number of equivalent hydropens number...
Consider the following nonlinear program: min s.t. - (a) Express the objective function of the above problem in the standard quadratic function form: (b) Find the gradient and the Hessian of f(x). (c) If possible, solve the minimisation problem and give reasons why the solution you found is a global minimum rather than just a local minimum. Otherwise, demonstrate that the problem is unbounded. f (x: y) = (x + 2y)2-2x-y We were unable to transcribe this imageWe were unable...
Let X1, X2, X3 ∼(iid) Exponential(λ). (a) Show that T(X1, X2, X3) = X1 + X2 + X3 is a sufficient statistic for λ. (b) Find the MVUE for λ. (c) Show that is not a sufficient statistic for λ. (d) Let = and find . Give an argument for why is not the best estimator of λ. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
Derive the moment generating function of y= a x1+b x2, where y~ N( a 1 + b2 , a2 12 +b222 + 2ab cov(x1, x2) ), not both a and b equal to zero. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Investigation 4: Quadratic Equations The quadratic equation is typically written in the form and has the solution 2a In this Investigation, we will look at a number of equations, rearrange them to be in this form, and identify which variables correspond to a, b, c, & x in the definition above. Activity 1-8: For each of the expressions, do the following Is it absolutely necessa ry to use the quadratic equation to solve the expression? . egardless of whether you...
Let be an inner product space (over or ), and . Prove that is an eigenvalue of if and only if (the conjugate of ) is an eigenvalue of (the adjoint of ). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageTEL(V) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about . For testing H0: = 10 vs H1: < 10, consider the statistic T- = Ri+ (1-i), where i =1 if Xi>10 , 0 otherwise; and Ri+ is the rank of (Xi - 10) among |X1 -10|, |X2-10|......|Xn -10|. 1. Find the null mean and variance of T- . 2. Find the exact null distribution of T- for n=5. We were unable to transcribe this imageWe were...
4. Suppose that X1, X2, . . . , Xn are i.i.d. random variables with density function f(x) = 0 < x < 1, > 0 a) Find a sufficient statistic for . Is the statistic minimal sufficient? b) Find the MLE for and verify that it is a function of the statistic in a) c) Find IX() and hence give the CRLB for an unbiased estimator of . pdf means probability distribution function We were unable to transcribe this...
(of I assume) 1 is not a quadratic residue If p 4k3 for some positive integer k, then We were unable to transcribe this image 1 is not a quadratic residue If p 4k3 for some positive integer k, then