Let X and Y be independent exponentially distributed random variables, each with mean 1. Find P[X>Y|X<2Y]
I know I must use conditional probability, but I can't simplify it enough to integrate.
Consider the partial differential equation 2dz/dx-dz/dy=0
Show that if f(u) is a differential function of one variable, then the partial differential equation is satisfied by z=f(x+2y)
3. The Attempt at a Solution : Change of variables? No idea :S
Well for instance f(x,y,z)=xy+xz+xyz. Then the level surface f=10 would be xy+xz+xyz=10. I am just wondering whether this level surface will influence the equation of the tangent plane. If so, how do I find it with respect to that level surface.
Homework Statement
Does the surface level of a curve influence the tangent plane of that curve? If so, how do I find the tangent plane specific to that level?