Question

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?

Answer 1

use this it may help 'cos ur question it not that clear

Answer 2

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.

Answer 3

the probability of geting is 1/8

Answer 4

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)?

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

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