Explain RANDOM VARIABLE in detail. DISCRETE and CONTINOUS All. with EXAMPLES?

Answer 1

RANDOM VARIABLE .....
http://en.wikipedia.org/wiki/Random_Variable
Examples
A random variable can be used to describe the process of rolling a fair die and the possible outcomes { 1, 2, 3, 4, 5, 6 }. The most obvious representation is to take this set as the sample space, the probability measure to be uniform measure, and the function to be the identity function.

For a coin toss, a suitable space of possible outcomes is Ω = { H, T } (for heads and tails). An example random variable on this space is.........
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DISCRETE VARIABLE .....
http://en.wikipedia.org/wiki/Discrete_variable
For a discrete random variable X, let u0, u1, ... be the values it can assume with non-zero probability. Denote

These are disjoint sets, and by formula (1)

It follows that the probability that X assumes any value except for u0, u1, ... is zero, and thus one can write X as

except on a set of probability zero, where and 1A is the indicator function of A. This may serve as an alternative definition of discrete random variables.
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CONTINOUS RANDOM VARIABLE
http://en.wikipedia.org/wiki/Continuous_Random_Variable

I'm just copying and pasting this stuff.
but I put the link here for you to go to to read more on it.
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EDIT:
more...with examples
Random Samples: http://www.mathsrevision.net/alevel/pages.php?page=68

discrete random variables:
http://www.mathsrevision.net/alevel/statistics/discrete_random_variables.php

continuous random variable:
http://www.mathsrevision.net/alevel/pages.php?page=52

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http://stattrek.com/Lesson2/DiscreteContinuous.aspx

http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html

Answer 2

A random variable is one whose value is not known 'a priori' and which has no known correlation with any of the other variables in the experiment.
A 'discrete' random variable can assume only a finite number of values (such as the number of people in an elevator) while a 'continuous' random variable may have any of a continuous number of values (the speed of an object).

Doug

Answer 3

A random variable is a numerically-valued FUNCTION defined over a sample space (meaning it usually has limits). It is a link between a sample space and a range.
A discrete random variable is an integer that can assume only countable values. Usually a count of something.
A continuous random variable is usually a measurement and can take on an infinity (uncountable) number of values.

Answer 4

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Answer 5

Try here: http://en.wikipedia.org/wiki/Random_variable