If (X, Y) is uniformly distributed over the semicircle bounded by y = 1-x? and y = 0, find E(X/Y) and E(Y/X). Also verify the E{E(X/Y)} = E(X) and E{E(Y/ X)} = E(Y). %3D
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- If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s diagonals iss = √(x2 + y2 + z2). How is ds/dt related to dy/dt and dz/dt if x is constant?Show that if φ is continuously differentiable in a given region V and on itsboundary S, then∫S φ dS =∫V ∇φ dVIf supX∈S ||X||p 1, then S is uniformly integrable.
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