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

the probability of geting is 1/8

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