(1 C) Suppose n()-e. Find a differential operator L (other than Ly)-0) such that L(yi)-0
Find the solution of the differential equation 6y-1 ly, +3y = 0 Find the solution of the differential equation 6y-1 ly, +3y = 0
Find the eigenvalues and eigenfunctions for the differential operator L(y)=−y″L(y)=−y″ with boundary conditions y′(0)=0y′(0)=0 and y′(3)=0y′(3)=0, which is equivalent to the following BVP y″+λy=0,y′(0)=0,y′(3)=0.y″+λy=0,y′(0)=0,y′(3)=0. Find the eigenvalues and eigenfunctions for the differential operator L(y)--y" with boundary conditions y (0)0 and y' (3)-0, which is equivalent to the following BVP (a) Find all eigenvalues 2n as function of a positive integer n > 1. (b) Find the eigenfunctions yn corresponding to the eigenvaluesn found in part (a). Help Entering Answers ew...
1.2 Let Yi and Y2 be independent random variables with Yi N(0, 1) and Y2 N(3,4). (a) What is the distribution of Y?? (b) If y-l (Y2-3)/2 | , obtain an expression for уту. What is its Yi and its distribution is yMVN(u, V), obtain an expression for yTV-ly. What is its distribution?
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6 Other solutions (ODEs). Please help. Thank you. One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b) One...
1 point If the series y(x)s c,x" is a solution of the differential equation 3y" 4x2y' + ly-0, then c.. cn,n 1,2,... C,N A general solution of the same equation can be written as y(x)-Coyix)+ciy2(x), where x)a" n-2 Calculate 1 point If the series y(x)s c,x" is a solution of the differential equation 3y" 4x2y' + ly-0, then c.. cn,n 1,2,... C,N A general solution of the same equation can be written as y(x)-Coyix)+ciy2(x), where x)a" n-2 Calculate
(1 point) Let y" + ly' – 12y=0. a. Try a solution of the form y=e", for some unknown constant r, by substituting it into the differential equation. = 0. help (formulas) b. Simplify and factor your equation in the previous part as much as possible. Be sure to divide out any factors guaranteed to be nonzero. = 0. help (formulas) c. Find all values of r such that y=e" satisfies the differential equation. If there is more than one...
5.26 Suppose that y is N, (μ, 2), where μ LJ and -σ2ρ for all Thus E(yi-μ for all i, var(yi) 0" for all i, and cov(yoy ij; that is, the y's are equicorrelated. (a) Show that Σ can be written in the form Σ-σ2(I-P)1+a (b) Show that Σ-i(vi-y?/(r2(1-p] is X2(n-1) 5.26 Suppose that y is N, (μ, 2), where μ LJ and -σ2ρ for all Thus E(yi-μ for all i, var(yi) 0" for all i, and cov(yoy ij; that...
Suppose you have a random sample yi, i = 1, ..., n, from a distribution such that E[yi) = 0 and Var(yi) = 02. - Yi is the sample (i.) Find the asymptotic distribution of ny, where y = average. (ii.) Find the asymptotic distribution of C(GP) = ?. Is C(02) asymptotically pivotal for o2? Explain. (iii.) Using the result in (ii) provide an asymptotic 95% confidence interval for o(if you did not find the asymptotic distribution at point (ii)...
Given y'"- y" - 4y'- 6y=0 (1) , identify Differential Operator L of (1). OL=D3-D2 - 4D - 6 o L = (D - 3)(D2 + 2D + 2) O Both of them are correct! None of them
Given y'"'- y" - 4y'-6y=0 (1) , identify Differential Operator Lof (1). o L = D3 - D2 - 4D - 6 O None of them o L = (D - 3)(D2 + 2D + 2) Both of them are correct!