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Suppose I throw 2 fair dice. Let X be a random variable of the total points from the 2 fair dice thrown. So, the random value X can hold 11 values from 2 to 12:
\[X=\{ 2,3,...,12\]
As usual in textbooks, there is often another omega in the sample space like this:
\[\omega \in \Omega \]
In my case, what are the values in my space space of capital Omega? And what are my sampling values?
 2 years ago
 2 years ago
Suppose I throw 2 fair dice. Let X be a random variable of the total points from the 2 fair dice thrown. So, the random value X can hold 11 values from 2 to 12: \[X=\{ 2,3,...,12\] As usual in textbooks, there is often another omega in the sample space like this: \[\omega \in \Omega \] In my case, what are the values in my space space of capital Omega? And what are my sampling values?
 2 years ago
 2 years ago

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xEnOnnBest ResponseYou've already chosen the best response.0
In my case, what are the values in my sample space of capital Omega? And what are my sampling values?
 2 years ago

ash2326Best ResponseYou've already chosen the best response.0
\(\omega \)={2,3,4,5,6,7,8,9,10,11,12} I think Ω is {1,2,3,4,5,6,7,8,9,10,11,12}
 2 years ago

xEnOnnBest ResponseYou've already chosen the best response.0
Are ω the sampling values? Also, since X is a random variable, which is a function by itself, for this: \[X(\omega )=x\] How would I match the values? Suppose I have X(12), what should the output of X(12) be?
 2 years ago

xEnOnnBest ResponseYou've already chosen the best response.0
When I have X(a)=b, 'a' is the random variable value, which is the total points I get out of the 2 dice, is this right? And what about 'b'? What does it mean for 'b'?
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
a is an element from the sample space...b is a possible value of the random variable
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
You should probably treat it like this... roll two die then the sample space consists of 6*6=36 different ordered pairs let X be the random variable that add the ordered pairs then \(\omega\) is an ordered pair and X is a random variable taking values in {2,3,...,12}
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
so if \(\omega=(2,5)\), \(X(\omega)=7\)
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
X is a measurable function from the sample space to the real line
 2 years ago

xEnOnnBest ResponseYou've already chosen the best response.0
ohhh..... Thank you so much!! This very clear. Thanks a lot!
 2 years ago

xEnOnnBest ResponseYou've already chosen the best response.0
Which also means, I cannot write as X(12) because there isn't such a thing. It should be X({6,6})
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
To be completly correct...yes....some times people will say that the experament is to roll two die and add them ... then one could look at X(12) it is better (and correct) to treat the two die rolls as the experament and then get ordered pairs...then let the random variable add them
 2 years ago

xEnOnnBest ResponseYou've already chosen the best response.0
Now I understand. Thank you so much! It is very clear! :)
 2 years ago
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