1) (15 pts) Random variables X and Y have joint PDF: 16e (2x+3) x20, y 20...
#5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1 #5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1
7.5.6 Random variables X and Y have joint PDF fx,y(x, y) = _J1/2 -1 < x <y <1, 1/2 10 otherwise. (a) What is fy(y)? (b) What is fx|v(x\y)? (c) What is E[X|Y = y)?
Problem 3: (15 points) The random variables X and Y have the joint PDF otherwise 1) Determine the marginal PDFs fx(x) and fy (y) 2 Determine EX and E[Y: 3) Determine Cov[X, Y]
4.5.4 X and Y are random variables with the joint PDF ( 5x2/2 JX,Y (x, y) = -1 < x < 1; 0 <y < x2, otherwise. 10 (a) What is the marginal PDF fx(x)? (6) What is the marginal PDF fy(y)?
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
dont have to do part C! The join pdf of random variables X and Y is given as JXY, fxx(x, y) = {e=(x+y) x>0, else y>0 0 a) (10 pts) Find marginal pdf fx(x) for X, fy(y) for Y, and plot fx(x) and fy(y) b) (10 pts) Are X and Y independent? Why? c) (15 pts) Find the mean of X, the mean of Y, E[XY). d) (10 pts) Find the probability of event {Osxsys1}
2. Let X and Y be two continuous random variables varying in accordance with the joint density function, fx.y(z, y-e(x + y) for 0 < z < y < 1. Solve the following problem s. (1) Find e, fx(a) and fy (v) (2) Find fx-u(z) and fY1Xux(y) (8) Find P(Y e (1/2, 1)|X -1/3) and P(Y e (1/2,2)| X 1/3). 3. Find P(X < 2Y) if fx.y(zw) = x + U for X and Y each defined over the unit...
For positive constant a and b, a pair of random variables has joint PDF specified by x.y(a,y)-abe-(ax+by) a. Find the joint CDF, Fx.y (x, y), b. Find the marginal PDFs, fx (x) and fy O) c. Find probability that X > Y d. Find probability that X > Y2
For positive constant a and b, a pair of random variables has joint PDF specified by x.y(a,y)-abe-(ax+by) a. Find the joint CDF, Fx.y (x, y), b. Find the marginal PDFs, fx (x) and fy O) c. Find probability that X > Y d. Find probability that X > Y2
3. Consider two random variables X and Y, whose joint density function is given as follows. Let T be the triangle with vertices (0,0), (2,0), and (0,1). Then if (x, y for some constant K (a) (2 pts.) Find the constant K (b) (4 pts.) Find P(X +Y< 1) and P(X > Y). (c) (4 pts.) Find the marginal densities fx and fy. Conclude that X and Y are not independent