Question

in probability what does E[|X|] mean? I know that |X| means cardinality but what does |X| mean when we use it in sense of probability?

Answer 1

you can also find this symbol at http://en.wikipedia.org/wiki/Expected_value

Answer 2

Isn't that random variable ?

Answer 3

sorry I mean absolute value instead of cardinality in the original question****

Answer 4

yes X is a random variable but when we use perpendicular bars | | in E[|X|] then what does it mean?

Answer 5

That is the absolute value of the random variable for expectation that is E..

Answer 6

OK @waterineyes Also, in martingale when we use E[X_n+1 || F_n] = X_n then the two perpendicular bars || denotes conditional probability or what?

Answer 7

Conditional Probability is shown by one bar only I think..
Like this :

\[P(A|B)\]

Answer 8

yeah that I know but when we use || then what does it mean?

Answer 9

This is sign for Absolute Value...

Answer 10

Suppose :

|x| = 5y + 6

So here, to eliminate bars from x:

There will form two equations:

|x| = 5y + 6 gives x = 5y + 6 as first equation..

|x| = 5y + 6 gives -x = 5y + 6 as second equation...

Answer 11

I do understand the concept of absolute value but I don't understand the meaning of || in ecepectation

Answer 12

I am explaining it in terms of math..

But in probability the concept is same..

Answer 13

In that link read the column named "INEQUALITY"