
check if
e-1/4/ f(x) if x > 0 if x < 0 is differentiable at 0.
Problem 2. Let f be a self-map on a set X. For x,y e X define x ~ y if and only if f"(x) = f(y) for some integers n, m > 0. Show that ~ is an equivalence relation.
this curve,
with X - axis rotation, calculate surfacea area
y=e-72, (x > 0)
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.
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
7. Suppose X and Y have joint pdf f(x,y) = 24x y if x >0, y>0,x+y<1 and 0 otherwise. Find P(Y > 2x).
(a) For what value of x does f(x) = g(x)? (b) For which values of x is f(x) >g(x)? For every x in the interval f(x)>g(x). (Type your answer in interval notation.) In parts (a) and (b), use the given figure. (a) Solve the equation: f(x) = g(x). (b) Solve the inequality f(x) > g(x). у y = g(x) y = f(xN (-9,7)
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?