Can a continuous variable be finite?

Can a continuous variable be finite?

Continuous variable is infinite and uncountable.

Are continuous random variables infinite?

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 the sample space of a continuous random variable?

The domain of a random variable is called a sample space, defined as the set of possible outcomes of a non-deterministic event. For example, in the event of a coin toss, only two possible outcomes are possible: heads or tails.

What is the probability of a continuous random variable?

zero
A continuous random variable can take on an infinite number of values. The probability that it will equal a specific value (such as a) is always zero.

What is a finite random variable?

A random variable that may assume only a finite number or an infinite sequence of values is said to be discrete; one that may assume any value in some interval on the real number line is said to be continuous. This function provides the probability for each value of the random variable.

Can discrete random variable be infinite?

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

Why is the probability of a continuous random variable 0?

The probability of a specific value of a continuous random variable will be zero because the area under a point is zero.

What is a finite sample space?

If a sample space contains a finite number of elements, then the sample space is said to be a finite sample space. The sample space for the experiment of a toss of a coin is a finite sample space. It has only two sample points.

How do you find the continuous random variable?

Let X be a continuous random variable with PDF given by fX(x)=12e−|x|,for all x∈R. If Y=X2, find the CDF of Y. =1−e−√y….Solution

1. To find c, we can use ∫∞−∞fX(u)du=1: =∫∞−∞fX(u)du. =∫1−1cu2du.
2. To find EX, we can write. EX. =∫1−1ufX(u)du.
3. To find P(X≥12), we can write P(X≥12)=32∫112x2dx=716.

How do you find the probability of a continuous random variable?

The probability distribution of a continuous random variable X is an assignment of probabilities to intervals of decimal numbers using a function f(x), called a density function, in the following way: the probability that X assumes a value in the interval [a,b] is equal to the area of the region that is bounded above …

How do you calculate continuous probability?

For a continuous probability distribution, probability is calculated by taking the area under the graph of the probability density function, written f(x). For the uniform probability distribution, the probability density function is given by f(x)= { 1 b − a for a ≤ x ≤ b 0 elsewhere .

How do you tell if a random variable is discrete or continuous?

A discrete variable is a variable whose value is obtained by counting. A continuous variable is a variable whose value is obtained by measuring. A random variable is a variable whose value is a numerical outcome of a random phenomenon. A discrete random variable X has a countable number of possible values.

What is the difference between a random variable and sample space?

A sample space is a collection of all possible outcomes of a random experiment. A random variable is a function defined on a sample space. We shall consider several examples shortly. Later on we shall introduce probability functions on the sample spaces.

What is a random variable?

A random variable is a function defined on a sample space. We shall consider several examples shortly. Later on we shall introduce probability functions on the sample spaces. A sample space may be finite or infinite. Infinite sample spaces may be discrete or continuous. Tossing a coin.

What is a sample space in probability?

Before understanding the concept of random variables, you need to know what is a sample space in probability. The range of all possible outcomes of an experiment is known as the ‘Sample Space’ (s).

Is the sample space finite or infinite?

A sample space may be finite or infinite. Infinite sample spaces may be discrete or continuous. Tossing a coin. The experiment is tossing a coin (or any other object with two distinct sides.) The coin may land and stay on the edge, but this event is so enormously unlikely as to be considered impossible and be disregarded.