={Ke−3x−2y0
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Suppose the JPDF of X, Y is
f(x,y)={Ke−3x−2y0<x,x<y0otherwisef(x,y)={Ke−3x−2y0<x,x<y0otherwise give clear working of the following questions.
i) Find K so that f(x,y)f(x,y) is a valid jpdf.
For correct value of K, so that f(x,y)f(x,y) is a valid jpdf;
ii) Find E[X]E[X],
iii) Find E[Y]E[Y],
iv) Find E[XY]E[XY]
v) Find Cov[X,Y]Cov[X,Y]
vi) Are the random variables X and Y are independent? Why or why not?
Also use the working in this question to answer the following five questions.
Step by step
Solved in 4 steps with 3 images
- Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii a1=0.1 11. Consider the function f(x)=4x2(1x) a. Find any equilibrium points where f(x)=x. b. Determine the derivative at each of the equilibrium points found in part a. c. What does the theorem on the Stability of Equilibrium points tell us about each of the equilibrium points found in part a? d. Find the next four iterations of the function for the following starting values. i. a1=0.4. ii. a2=0.7 e. Describe the behavior of successive iteration found in part d. f. Discuss how the behavior found in part d relates to the results from part c.Find f, and f, and evaluate each at the given point. 'y' f(x, у) %3D е\у?, (In 3, 2) f,(x, y) = fy(x, y) = f(In 3, 2) fy(In 3, 2)
- Eliminate the arbitrary constant for y = 4 + Cje3 %3D Oy' + 3y + 12 = 0 Oy' - 3y + 12 = 0 %3D O y" – 3y + 12 = 0 %3D O y" + 3y +12 = 0Find V. (V x F), if F(x, y, z) = 5e**i+ 5xe"j – 7ek. V·(V × F)function fo) = 7X0+)0xt-10x3_4 Qn Antiderivative of fa is F(x) = Axn+ Bxm, CxPrDx8 A= 710 where cis -%/- and Pis 4 Dis -4 andg Bis and m is
- Find V. (V x F), if F(x, y, z) = 7e**i+ 6xe"j – 2ek. V.(V x F) = 0The equations ry? + 8zzcos(u) + ye" = 16 and r*yz + xe" – 5u²v² = 15 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find (),y at P. %3DLet f(x,y)= x'y+2x² and find f,(1,2) and f,(1,2) 1. 3x- y