What's the difference between discrete random variables and continuous random variable?

Can anyone explain me clearly.

I will appreciate it thanks.

Hello,

Random Variables

A discrete random variable is one that takes on a integer value. We use discrete random variables for objects that can not be anything but a whole number: number of cars passing through a toll booth, number of students in a class, the age of students in a class, days that go by before you see rain. . .etc. etc. A continuous random variable is a variable that can take on any real value (on an interval): average volume of a soda can, days that go by before you see rain, height of students, length of a sheet of paper. You'll notice that for continuous random variables, they are mostly measurements made of time and space, whereas discrete random variables will usually be countable objects.

Another interesting difference between discrete and continuous random variables, is how we define P(X=x), and F(X=x) for discrete and continuous random variables respectively. For discrete random variables, we simply look at the probability of obtaining that single value, which can be done by looking at a frequency distribution chart, or the probability mass function (just the chart listing the individual probabilities of "x" occurring).

For continuous random variables, the probability of selecting a single value out of the entire sample is zero. Why? Simply goes back to how we define a continuous random variable and the probability density function (the same principle as the probability mass function) of it: a continuous distribution is just that, a continuous, integrable line defined by a function f(x) - f(x) in this case is the curve that represents the distribution of our continuous random variables. As the area under a probability curve is the probability of selecting a random variable that falls into that area, if we wanted to find the probability of selecting a single random variable and the area underneath what would our integral look like:

$\displaystyle P(X=x)\int_x^x f(x) dx$

Regardless of what kind of function you have, you already know what that result would be.

Of course there are more particulars and interesting behaviors of random variables, but those are two of the most basic defining things about the two classes of random variables.

ANDS!,

Originally Posted by ANDS!

A discrete random variable is one that takes on a integer value.

And something that takes 1/2 and 1/4, is it a discrete random variable ? Because they're not integers
A discrete rv is a rv that takes a countable number of values.

We use discrete random variables for objects that can not be anything but a whole number: number of cars passing through a toll booth, number of students in a class, the age of students in a class, days that go by before you see rain. . .etc. etc.

That's a tad reductive, as said before, it's not necessarily a whole number.

Another interesting difference between discrete and continuous random variables, is how we define P(X=x), and F(X=x) for discrete and continuous random variables respectively.

What's that ?