F'(x) < 0 if 0<x< 2or x > 4 f"(x)>0if1<x<3, F"(x)<0if x<lor x>3 4. Find the...
Please write clear and put the answer between square If 31 - 3 < f(x) < 22 - 32 + 6 for 1>0, find lim f(x) 293 For the function g whose graph is given, state the following, lim g(x)= lim g(x)=
X+2 X<3 n. lim f(x), where f(x)= { x3 12-2x x>3 3
Question 9 Find 5x+1 f(x) dx given that f(x) = { 3-x 0<x< 1 1<x<3 =la ole ala ala T
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
4. (30 pts) Let (X,Y) have joint pdf given by < , | e-9, 0 < x < f(x,y) = 3 | 0, 0.w., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
Given f(x,y) = 2 ; 0 <X<y< 1 a. Prove that f(x,y) is a joint pdf b. Find the correlation coefficient of X and Y
Suppose f'(x) = -1/3(x+3). On what open interval(s) is f(x) decreasing 0-3 < < 0 0-3 <x<0 0 - < I< -3 0 - < ?<-3 and 0 < x < 0
NIS 4) The joint pdf of X and Y is 1, 0<x<1, 0<y< 2x, fx,8(8,y) = { 0, otherwise. otherwise. or 1 (Note: This pdf is positive (having the value 1) on a triangular region in the first quadrant having area 1.) Give the cdf of V = min{X, Y}. x
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
3. Find the limit. lim X+0 (Inx)2 x (4 pts) exe-x-2x X-sin 4. Find the limit. lim * (4 pts)