Can someone solve this pleases?

[hannah.ek94]

Ex/ find the equation of the system of surfaces which cut orthogonal the system x^2+y^2+z^2=c*x*y where c is constant in which passing through the circle x^2+y^2=4 and z=1

Example/ x and y are jointly continuous with
f(x,y)={c*x*y ; x≥0 , y≥0 , x+y≤1
0 other wise }
1/find c
2/find marginal p.d.f. of x and y
3/E(xy)
4/cov(x,y)

 

[Deleted member 4993]

Ex/ find the equation of the system of surfaces which cut orthogonal the system x^2+y^2+z^2=c*x*y where c is constant in which passing through the circle x^2+y^2=4 and z=1

Example/ x and y are jointly continuous with
f(x,y)={c*x*y ; x≥0 , y≥0 , x+y≤1
0 other wise }
1/find c
2/find marginal p.d.f. of x and y
3/E(xy)
4/cov(x,y)

What are your thoughts?

Please share your work with us ...

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[hannah.ek94]

What are your thoughts?

Please share your work with us ...

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Well I study mathematics degree in Irbil, Kurdistan (Iraq) and i'm in my third year (1st year was foundation). The problem above is given to me by my professor without any explanation or examples to help us wok it out. I know you may not be aware but its probably silliest thing to study such high degree here with the limited support and guidance.

I will really appreciate it if you could have a go at the problem because i don't know where to start or maybe you can solve me a similar example. Thank you

 

[HallsofIvy]

Your "example" doesn't seem to have any relation to your stated problem! The stated problem is a problem in finding "orthogonal trajectories", a typical "Calculus III" problem, while your example deals with probability distributions. Are you sure they go together?

In any case, what you want to do is take derivatives to get a differential equation, or differential equations, describing your family of surfaces, use the fact that "orthogonal trajectories", curves that are perpendicular to those surfaces, have slope -1/m where "m" is the slope of the given trajectories, the solve those new differential equations.