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[Agent Anderson]

Could someone just explain what the colons and arrows mean?



The unfamiliar notation seems to be the hardest part about this class.


EDIT: Also, does someone have a better explanation of an image?

[Technomancer]

The term "X:W->R" indicates that X is a random variable over the sample space W. Any actual realization of the variable X is a member of set R (which in this case is the set of real numbers). The notation in the second line is a bit eccentric, and the ':' is more often written as '|', which simply means 'such that.' In other words, read it as 's is an element of W, such that X(s)>2'.

You tend to see this notation a lot when dealing with functions or transformations. The meaning is similar, except that you are not dealing with random variables. In such a case "X:W->R" would read 'The transformation X operates on a member of set W transforming it to a member of set R'

The "image" of a transformation (or random variable) is the same as its range. In other words it is the set of all values that a realization of X may take on.
http://mathworld.wolfram.com/Image.html

[Agent Anderson]

Thanks.