A random variable is a way to mathematically express steady acoustic outcomes as real numbers.
So a random variable is really a functional mapping that maps a set of experimental outcomes, such
as rolls of dice to a set of real numbers, such as one, two, three.
So we can mathematically write this using this equation here.
Now, this X here, this is the random variable and we can write it saying that it is a mapping between
the set of possible outcomes s and a set of real numbers.
Now, when we say real numbers, we can mean continuous numbers.
So it could be any number along the number line.
So any fractional number, any hole number.
So it could be one point one, three point one.
So it's just a continuous spectrum of numbers.
It could also be a discrete set.
So it could be integer values such as one, two, three.
We can put this into more of a concrete concept by let's looking at an example, so let's let expe the
random variable for a toss of the dice.
So in this case, this is going to be a different outcomes when may roll the dice, we can get one,
two, three dot all the way up to six dots showing on the up face.
So these are the different outcomes of the experiment.
Now, we have no real numbers you want to represent as the outcome.
So this is going to be this great set and the set of set for is just going to be one, two, three,
four, five.
And basically what the random variable is doing, it's just going to map the outcomes to the real numbers.
So obviously for convenience, say we're going to map the one to number one, we're going to map two
dots to number two, and they're going to go through and do that for all the different outcomes to all
the different discrete numbers.
Now, there's no reason why we couldn't have this map the other way.
We could have done it.
We could have set a single dot is six.
Two dots is five.
We could have done it in reverse order.
It doesn't matter.
Doesn't matter.
It's just the way that we've used to express the mapping.
So the random variable X has a possibility of being any of the real numbers in a.
Once the experiment is run, i.e., we toss a dice or we flip the coin once it has been carried out,
then the value of the random variable or outcome has been determined.
So if we roll the dice, we don't know what's going to be.
But once it lands, then it becomes the number, it becomes the outcome.
So in this case, it becomes five once it's become Disvalue five, once the outcome has been determined
that it is the random value as just a normal algebraic value.
So it's only it's only non-deterministic before the experiment is run.
Once the experiment is run, the value becomes set and it becomes deterministic and we can just treat
it like any other variable in an equation.