Earlier than giving a definition for discrete random variable, allow us to outline what a random variable is.

A random variable is a variable that has precisely 1 numerical worth and this worth is set by the result of a random experiment.

For instance, the variety of autos somebody owns is a random variable. To seek out out, you will have to randomly choose individuals and ask. Suppose you ask 200 individuals and 40 individuals say that they do not personal a automotive, 100 individuals say they personal 1, and 60 individuals say they personal 2.

Let x be the variety of autos owned by somebody chosen randomly. Then, based mostly on our outcome, x might be 0, 1, or 2.

For the reason that worth of x is determined by the result of a random experiment or asking individuals randomly, x known as random variable or probability variable.

What’s a discrete random variable then?

A random variable that assumes values which might be distinct and countable known as discrete random variable.

Why are the values distinct? Utilizing the instance above, somebody can both personal 0 automobile, 1 autos, or 2 autos. These values are clearly distinct or completely different. 1 is just not the identical as 0, 1 is just not the identical as 2, and 0 is just not the identical as 2.

Why are the values countable? It’s as a result of we will rely them : 0, 1, and a couple of. There are 3 completely different values and we had been capable of rely with none issues.

Different examples of discrete random variables

  • The variety of prospects visiting a retailer throughout any given hour.
  • The variety of TVs an individual owns.
  • The quantity you get while you roll a die.
  • The variety of tails obtained in three tosses of a coin.
  • The variety of auto accidents that happen in a metropolis throughout per week.

Discover that the variety of prospects visiting the shop will give distinct values. The variety of individuals visiting might be 0, 1, 2, 3, 4, 5, … and as soon as once more we will nonetheless rely.

Discover additionally that for those who toss a coin 3 instances, you might get 0 teal, 1 tail, 2 tails, or 3 tails.

In our instance above about variety of autos somebody owns, we discovered 3 distinct values {0, 1, 2}. That is straightforward to rely since we’re coping with a finite variety of values.

A random variable can nonetheless be discrete with infinitely many values so long as we will rely these values or create an inventory.

For instance, Let x be the variety of prospects visiting a retailer without end and ever

This record may be very very massive, however the record remains to be countable for those who might reside without end. This can after all take you without end and ever to rely, however it is possible for you to to rely for those who by no means die!

A discrete random variable both has a finite variety of values or a countable variety of values even when it takes eternity to rely.

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