If you have the first two conditions given, then you can conclude that

and

has the same distribution, which is slightly differ from the third condition.

On the other hand, if the third condition is given, then given any one of the first two condition, we can conclude the other condition hold.

The location-scale transformation is quite standard here. In multivariate case, see e.g.

http://en.wikipedia.org/wiki/Multiva...transformation