I am trying to understand Random Variables.
Please do let me know if my definiton is correct - or I have got things mixed up.
1. Let be the sample space i.e. set of all possible outcomes of an experiment; This can be countable or uncountable.
2. be the sample point i.e. a specific outcome of the experiment
A real valued random variable is a
And that is it !!
Informally for every , there is a unique
Is this definition correct / exact ?
Reason of my confusion is that some books define random variable as "a funciton which maps event in the given sample space to a real number." - I think this definition is wrong. Any comments?
I am trying to understand two concepts
1. E(X) - Expected value of X
2. E(X|A) - Conditional expectaion under event A
I think in 2 above, we have not changed the way X was defined on the sample space, only thing that changed is probabiltiy measure - Is this understanding correct?
Please help - Any references would be welcome