# What is Independence: Definition and 354 Discussions

Independence is a condition of a person, nation, country, or state in which its residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory. The opposite of independence is the status of a dependent territory.

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1. ### I The third central moment of a sum of two independent random variables

Is it true that when X and Y are independent, E ({X+Y}3) = E (X3)+E(Y3)?

46. ### I Vector components, scalars & coordinate independence

This question really pertains to motivating why vectors have components whereas scalar functions do not, and why the components of a given vector transform under a coordinate transformation/ change of basis, while scalar functions transform trivially (i.e. ##\phi'(x')=\phi(x)##). In my more...
47. ### Is a force field like the one in Independence Day possible in real life?

When the US fighter aircraft fire on the alien spacecraft , the pilots learn that the spacecraft is protected by some type of an invisible force field. Does our current understanding of how the universe works allow for such a thing?
48. ### Path Independence: Solving a Physics Problem

Homework Statement Hi,I am trying to understand the proof attached. My problem is shown by a red arrow.Can someone explain those 2 steps? And please answer it as simply as you can...Since I haven't done multivariable calculus..It is a physics course.Thanks Homework EquationsThe Attempt at a...
49. ### I Independence of speed of light and velocity of source

I've been attempting to learn special relativity, but I've encountered a stumbling block. I understand that the speed of light is independent of the speed of the source of the light (similar to how sound waves travel at a speed that is independent of the speed of the energy source of those...
50. ### MHB How can the Wronskian be used to determine linear independence?

I'm asked to check whether $\left\{1, e^{ax}, e^{bx}\right\}$ is linearly independent over $\mathbb{R}$ if $a \ne b$, and compute the dimension of the subspace spanned by it. Google said the easiest way to do this is something called the Wronskian. Is this how you do it? The matrix is: \$...