Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).
Consider the following differential equation. Assume that all eigenvalues are real y" + λy 0, y(0) 0, y(n) + y'(n) 0 (a) Determine the form of the eigenfunctions n(x)-cos μηχ, where u2- O φ n(x)-1-μ tan(A), where-u2-λ 0 φ n(x)-sin μηχ, where μ2-λ O φ n(x)-1-μ cot(A), where-μ2-λ O φη(x) = 1-μ cot(A), where μ = λ Determine the determinantal equation satisfied by the nonzero eigenvalues O μη satisfies cot v/μ -V μ nn satisfies tan v/λπ-- νλ O An...
dz Find when u = 0, v = 2, if z = sin (xy)+xsin (y), x=u2 +2V2, and y= uv. du az = du 1 = 0, V=2 (Simplify your answer.)
a. Show = b. Show E{(X-EX)(Y-EY)}=E{(X-EX)Y}
Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer
y" + 4y' + 164 = u2(t) – 44(t) with initial conditions y(0) = 1 and y'(0) = 0. (b) (8 points) Find lim y(t) t-
Using the Laplace transform, solve the initial value problem 8. y(0)-0. y" + 4y-sint-u2" sin(t-2r), y(0)-0,
Suppose that EX-EY-0, var(X) = var(Y) = 1, and corr(X,Y) = 0.5. (i) Compute E3X -2Y]; and (ii) var(3X - 2Y) (ii) Compute E[X2]
2) (2 pt) For what values of beta do the utility functions ui(x, y) and u2(, y) represent the same demand a) ui (z,v)-1 + z + y ard u2(z, y) = (1 +z + y)β b) u(z,)y5 and u2(r, y)Bln(x)(1 B)ln()
Plot the functions x, x3, ex and ex over the interval 0 < x < 4. in MATLab a. rectangular paper b. on semilog paper (logarithm on the y-axis) c. on log-log paper Be sure to use an appropriate mesh of x values to get a smooth set of curves! Hint: check the documentation for these functions: plot, subplot, semilogy, loglog