Types of Random Variables and Bernoulli Random Variable

We have two types of a random variable:-

1. Discrete value or fixed value.

2. Continuous random variable.

1. Discrete-valued Random Variable:-

Here the value that a random variable gives us is fixed. Example:-

Let's say we toss two coins and Y is a random variable that counts how many times 2 head appears. It will give us a fixed number.

2.Continuous random variable.

Instead of having one fixed value, here they can have uncountable or infinite values.  Ex: The amount of rain, in inches, that falls in a randomly selected storm.


1. Discrete Random Variable:-

They are of three types:

  • Bernoulli Random Variable:-
  • Binomial Random Variable.
  • Poisson Random Variable.

1. Bernoulli Random Variable:-

Y is a random variable whose value can be either 0 or 1 and true or false. It can take only two value.

If we assign the probabilty with this ,

p(0) = P{Y= 0} = 1 −p,
p(1) = P{Y = 1} = p
where p, 0 <= p <= 1, is the probability that the trial is a “success.