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Bookmark or Share- How to find E(XY) when X and Y are NOT indepdant? - Physics ForumsWhen X and Y are not independent, the relationship between E(XY) and E(X)E(Y) is given by the formula E(XY) = E(X)E(Y) + Cov(X,Y), where Cov(X,Y) is the covariance between X and Y. This means that E(XY) is equal to the product of the expected values of X and Y plus their covariance.
- Examples which satistfy f(x+y)=f(x) + f(y) - Physics ForumsThe question states: Give two different examples of f:R->R such that f is continuous and satisfies f(x+y)=f(x)+f(y) for every x,y e R. Find all continuous functions f:R->R having this property. Justify your answer with a proof. I came up with one example: f(x)=ax then...
- What is the difference between dy/dx, Δy/Δx, δy/δx and ∂y/∂x?Δy/Δx : is the gradient of a line through two points on the curve y=f(x) δy/δx is the gradient of the line between two ponts on the curve y=f(x) which are close together ∂y/∂x is the gradient of the tangent through a point on the surface y=f(x,z,...) in the direction of the x axis.
- Proof of continuous. f(x+y)=f(x)+f(y) - Physics ForumsLet f be a real-valued function on R satisfying f(x+y)=f(x)+f(y) for all x,y in R. If f is continuous at some p in R, prove that f is continuous at every point of R. Proof: Suppose f(x) is continuous at p in R. Let p in R and e>0. Since f(x) is continuous at p we can say that for all e>0...
- Proof of the total differential of f(x,y)? - Physics ForumsThe total differential of a function f(x,y) is a measure of how much the function changes when both x and y vary. It takes into account the partial derivatives of the function with respect to both variables. How is the total differential of a function calculated? The total differential of a function f(x,y) is calculated using the following formula:
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