What is the meaning of a randon variable?
what is the actual meaning of a random variable? When things are referred to as X it can get a bit confusing as to what X is actually relating to and I know its prob something very simple but the stats I do has kind of progressed past the point of actually needing to state it. I need to be able to visualise what it is!
Answers:
The term Random Variable is really a bit of historical hangover. It is really a function mapping from a sample space to real numbers. However this doesn't shed much light on trying to visualise what is going on.
Try thinking of it this way.
You have a variable X but each time you take the value of X it changes. However the different values that X takes have pattern to them. For example if the variable X is 'value on top face of a rolled 6-sided die' then if you take enough readings you will get approximately equal numbers of 1, 2, 3, 4, 5, 6.
Or to take another example, suppose you say that the random variable X is 'height of children of a certain age in a village'. This will very likely have a Normal (or Gaussian) distribution. In this case it is as though you didn't know the names of any of the children, and all you could say was 'next child'. The value of the Random Variable X would not be completely random (no very small or very large values) but would vary from one child to the next. There wouldn't be any pattern from one child to the next, but when you looked at all the values you'd collected there would be a characteristic bell-curve.
Its when it is random & variable Durrr
IT IS A VISUAL PROBLEM THAT THE VARIABLE REFERRED TO IS ACTULLY RANDOM , X DOES NOT MATTER AS IT DO'ES NOT RELATE TO THE PROCESS
A random variable, such as X, can be any number within the limitations of the problem.
For example, if you were to roll a six sided die, and the outcome were labeled X, X could be any whole number from 1 to 6.
The X is merely a notation used to say that you don't know exactly what the outcome of a problem is. It is a placeholder that you can do mathematical operations on to simplify, solve, or interpret the problem better.
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Answers:
The term Random Variable is really a bit of historical hangover. It is really a function mapping from a sample space to real numbers. However this doesn't shed much light on trying to visualise what is going on.
Try thinking of it this way.
You have a variable X but each time you take the value of X it changes. However the different values that X takes have pattern to them. For example if the variable X is 'value on top face of a rolled 6-sided die' then if you take enough readings you will get approximately equal numbers of 1, 2, 3, 4, 5, 6.
Or to take another example, suppose you say that the random variable X is 'height of children of a certain age in a village'. This will very likely have a Normal (or Gaussian) distribution. In this case it is as though you didn't know the names of any of the children, and all you could say was 'next child'. The value of the Random Variable X would not be completely random (no very small or very large values) but would vary from one child to the next. There wouldn't be any pattern from one child to the next, but when you looked at all the values you'd collected there would be a characteristic bell-curve.
Its when it is random & variable Durrr
IT IS A VISUAL PROBLEM THAT THE VARIABLE REFERRED TO IS ACTULLY RANDOM , X DOES NOT MATTER AS IT DO'ES NOT RELATE TO THE PROCESS
A random variable, such as X, can be any number within the limitations of the problem.
For example, if you were to roll a six sided die, and the outcome were labeled X, X could be any whole number from 1 to 6.
The X is merely a notation used to say that you don't know exactly what the outcome of a problem is. It is a placeholder that you can do mathematical operations on to simplify, solve, or interpret the problem better.
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