(a) For what value of x does f(x) = g(x)? (b) For which values of x...
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute< x², x? >; 0 b) Find the “angle” between the two functions.
For what values of x is the function f(x) = x3 + 15 x2 + 63 x increasing? f(x) is increasing when z 〈 and when x>
5. Let F(x, y, z) = (yz, xz, xy) and define 2 Crin = {(x,y,z) : x2 + y2 = r2, 2 = h} Show that for any r > 0 and h ER, le F. dx = 0 Crih
Let f(x, y) 2e-(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFS of each?
6-4 (a) The function g(x) is monotone increasing and y = g(x). Show that F(x) if xy(x, y) =İF,(y) if y>g(x) y<g(x) xytty (b) Find Fxy(x, y) if g(x) is monotone decreasing.
Let f(x,y) = 12e-2(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFs of each?
Q3. Find the quantile function F-1 for F(r)-1-1-α, x > 1.
What is the solution of day 2 dy 1(1+1) dx² + xăx x² y = f(x = a) (a > 0). on the interval 0<x< 0, subject to the boundary conditions y(0) = y(0) = 0? / is a positive integer.
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)