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Suppose I flip a coin 3 times, let the Sample Space \[\Omega =\{ H,T\} \] And \[\omega \in \Omega \] Define a random variable of X to be the number of heads such that \[X\in \{ 0,1,2,3\} \] Now, when I say this: \[P(X=3)\] I believe it means that I want to know the probability of getting 3 heads in all the flips. Second, then when I say this: \[X(\omega )\], what does this mean? What am I trying to find? For example: \[X(3)\] Is \[X(3)=P(X=3)\] ? Are they the same?

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|dw:1329058306810:dw| use this it may help 'cos ur question it not that clear
thanks..maybe I should try phrasing my question again. I have a random variable X. Often, I see the random variable used this way: P(X=3) to denote that I want to find the probability of the event. In this case, the probability of getting 3 heads in all the flips. However, I have also seen the random variable X used this way: X(w). What is the meaning of this using it as X(w)? The random variable X somehow becomes a function and I don't understand what function is it representing.
the probability of geting is 1/8

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Like, what is the meaning when a random variable is used in the notation as X(3) for instance. Is X(3) the same as P(X=3)?
omega means the number of the events yes they mean p(x=3)
Really? But sometimes the usage doesn't seem like this. For example, it could be used like: \[X(\omega )=x\] Which in this case, it doesn't look like it mean p(x=w) because X can't even take w because w is in the sample space whereas X is in some other space that I don't know what it is but it definitely isn't the sample space.
omega in ur rquestion u've rep it lie [x=H,T],THIS IMPLIES THAT the number of heads and tails r assigned to to it for example if the number of heads is equal to 4 and tails 4 it means ur sample space=[omega=hhh,hht,tht.htt,thh,tht,tth,tttthen they can say to u wat is prob of getting 2 heads at the flip this X refers to the number of heads u suppose to find
ahh.. I see...Thank you so much!! :)

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