Suppose that the random variables X and Y have joint p.d.f.f(x,y)=\begin

Caelan 2021-10-25 Answered

Suppose that the random variables X and Y have joint p.d.f.
f(x,y)={kx(xy),0<x<2,x<y<x0,    elsewhere
Evaluate the constant k.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

pivonie8
Answered 2021-10-26 Author has 91 answers

Given :
f(x,y)={kx(xy),0<x<2,x<y<x0,    elsewhere
To find k
f(x,y)dxdy=1
=02xxkx(xy)dxdy=1
=02xxk(x2xy)dydx=1
=02k[x2yxy22]xxdx=1
=02k[x3x32+x3+x32]dx=1
=02k[2x3]dx=1
=2k[x44]02=1
=2k(4)=1
=k=18

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-21
A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force acting at 20.0 degree angle above the horizontal. The block is displaced 5.0 m, and the coefficient of kinetic friction is 0.3. Find the work done on the block by ; a) the 70.0 N force,b) the normal force, and c) the gravitational force. d) what is the increase in the internal energy of the block-surface system due to friction? e) find the total change in the kinetic energy of the block.
asked 2021-02-04

A 17.8 kg flood light in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole. A cable connected to the beam helps to support the light. (In thefigure, θ = 34.2 degrees. Find (A) The tension in the cable and (B) the horizontal and (C) vertical forces exerted on the beamby the pole.
image
(A) 320 N
(B) 250 N
(C) 0

asked 2020-10-28
A stone hangs by a fine thread from the ceiling,and a section of the same thread dangles from the bottom of the stone.If a person gives a sharp pull on the dangling thread,where is the thread likely to break:below the stone or above it?
asked 2021-05-04
Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height of 13 m into 35 cm. of water. Assuming that he stops just as he reaches the bottom of the water and estimating his mass to be 72 kg, find the magnitudes of the impulse on him from the water.
asked 2021-03-20
Consider a solution x1 of the linear system Ax=b. Justify the facts stated in parts (a) and (b):
a) If xh is a solution of the system Ax=0, then x1+xh is a solution of the system Ax=b.
b) If x2 is another solution of the system Ax=b, then x2x1 is a solution of the system Ax=0
asked 2020-11-01

Find the inverse Laplace transform f(t)=L1{F(s)} of each of the following functions.
(i)F(s)=2s+1s22s+1
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.
(ii)F(s)=3s+2s23s+2
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.
(iii)F(s)=3s2+4(s2+1)(s1)
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.

asked 2021-10-23

To calculate:
To simplify the expression 243813.

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question