Suppose that X and Y have a joint pdf f (x, y) = (2/3)(x + 1), for 0 < x < 1,0 < y < 1, zero otherwise. (a) Find fx(x) (b) Find fy (y) (c) Find f(y|x)

3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx fyy - (fxy)²

Find y as a function of a if y(1) = 2, y(1) = 1. y = r²y" + 7ry +9y = 2³,

Vipul

Decide if the following functions are linearly independent in the interval (-00, 00) f1(2) = 1+r, f2(x) = x, fa(x)=r? %3D

6

F = (2+-1) dt

Let f(x) = x - 5, g(x) = Vx, h(x) = x°, and j(x) = 3x. Express each of the functions given below as a composite involving one or more of f, g, h, and j (a) y = Vx - 5 (b) y = 3/x (c) y = x1/4 (d) y = 9x (e) y = V(x - 5)5 (f) y = (3x – 15)5

Find the 2nd derivative of y = 3x + 7x O 90x3 O 18x4+7 O 18x + 7 O 360x3 O 90x4

4. Examine if functions f(x) f, (x) =x², f;(x)=x² – 2x are linearly = x, independent.