How Do You Solve Joint Density Functions for Marginals and Expectations?

[im.4.who]

hiii every body

i have Home Work could some one help me to solve this Question" or give me the guide

X, Y and Z are continuous random variables with joint density


F(x,y,z)= {(3/32 x^2) y+[1/48(x+y)z For 0<x<2,
0<y<1
0<z<4
elswhere =0


1) find the marginal of x,y and z
2)find E(x), E(y) and E(z)

 

[John Creighto]

hiii every body

i have Home Work could some one help me to solve this Question" or give me the guide

X, Y and Z are continuous random variables with joint density


F(x,y,z)= {(3/32 x^2) y+[1/48(x+y)z For 0<x<2,
0<y<1
0<z<4
elswhere =0


1) find the marginal of x,y and z
2)find E(x), E(y) and E(z)

Someone shortly will tell you to post this in the homework section. To get the expectation of x integrate the x*F(x,y,z) over the domain. I forgot what the marginal is but looking at wikipedia it seems to be the distribution of a subset of the other random variables. So I presume to get the marginal in tems of x you integrate out the y and z variables.

 

[im.4.who]

John Creighto thank u dear

 

[im.4.who]

Apologize to forget to provide attempt part:

1) find the marginal of x,y and z:
i have try to integrate x and y together
then the result be numbers with i reintegrate z to find the result
i don't know if this way is true
2)find E(x), E(y) and E(z)
this question provide with 3 variable and i know only to solve by 2 variable

someone help me please