## xEnOnn 3 years ago 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?

1. REMAINDER

|dw:1329058306810:dw| use this it may help 'cos ur question it not that clear

2. xEnOnn

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.

3. REMAINDER

the probability of geting is 1/8

4. xEnOnn

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)?

5. REMAINDER

omega means the number of the events yes they mean p(x=3)

6. xEnOnn

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.

7. REMAINDER

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

8. xEnOnn

ahh.. I see...Thank you so much!! :)