How does covariance and correlation coefficient actually work?

[iVenky]

We all know that if the covariance is positive then it means that if one increases then the other one also increases. If the covariance is negative it is the other way round. I know to calculate the covariance and deduce the relation between them. But I don't get an intuitive feeling regarding this covariance. How does this actually work? An example would help me.

Thanks a lot.

 

[mathman]

Let X and Y be independent random variables. Let Z = X+Y, then Z is correlated with X and Y. This means that if X is large, the Z would likely be large, etc.

 

[Stephen Tashi]

. But I don't get an intuitive feeling regarding this covariance. How does this actually work? An example would help me.

You have to explain what you mean by "actually work". It isn't always helpful in solving real life problems!