• anonymous
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?
Mathematics

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