## Can a discrete random variable be infinite?

A discrete random variable is one that can assume only a finite, or countably infinite, number of distinct values.

## Can a discrete random variable be infinite number of values?

Some references state that continuous variables can take on an infinite number of values, but discrete variables cannot. This is incorrect. In some cases, discrete variables can take on only a finite number of values.

Can a random variable have infinite expectation?

Petersburg Paradox. In the Pascal’s Wager example, we dealt with random variables which could take on values such as ∞ or −∞ . It is not surprising that the expected value is infinite when infinity is a possible value. However, the expected value can be infinite, even if the random variable is finite-valued.

### What is discrete infinite?

The discrete infinity of language means unlimited productivity from the finite means as a major design feature of language (Irvine, 2014). Discreteness means that the boundary between linguistic symbols is clear.

### Is infinity a discrete number?

There are two different conceptions of infinity in foundations of mathematics and physics. One is set-theoretical or Cantorian, and regards an infinity (especially, continuum) as an enormous amount of discrete points or elements.

When a random variables can take an infinitely uncountable possible values is called?

Continuous Random Variables As a result, the random variable has an uncountable infinite number of possible values, all of which have probability 0, though ranges of such values can have nonzero probability.

#### What type of random variable is shown when the data can take infinitely many values?

continuous random variable
A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.

#### What is infinite variance?

Infinite variance happens when the integral (sum) defining the population variance increases beyond any finite bound as the limit is taken.

What is finite expectation?

Definition. A random variable X is called integrable (or has finite expectation) if both. E(X+) and E(X−) are finite.

## Can variance be infinite?

What is Infinite Variance? Models with infinite variance have right tails that extend to infinity. Variance is a measure of how spread out a distribution is. Distributions with infinite variance have fat upper tails that decrease at an extremely slow rate.

## Is infinity discrete or continuous?

Is continuous variable infinite?

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements.

### What is a discrete random variable?

A random variable is a variable taking on numerical values determined by the outcome of a random phenomenon. The probability distribution of a random variable x x tells us what the possible values of x x are and what probabilities are assigned to those values. A discrete random variable has a countable number of possible values.

### What is a continuous random variable?

A random variable X that can assume an unlimited number of variables in a given interval is called a Continuous Random variable. The probability density function provides probabilities for each value of a continuous random variable. It can be a formula or equation.

What is the probability mass function of a discrete random variable?

Knowing the probability mass function determines the discrete random variable, and we will understand the random variable by understanding its pmf. Probability mass functions satisfy the following properties: Let p p be the probability mass function of X X. p(x) ≥ 0 p ( x) ≥ 0 for all x x. ∑xp(x) = 1 ∑ x p ( x) = 1.

#### Did you know that a random variable is a function?

Did you know that a random variable is a function that assigns a real number with each outcome in the sample space? For example, imagine you toss a coin twice, so the sample space is {HH, HT, TH, TT}, where H represents heads, and T represents tails.