Any function is not a Random Variable

In summary, the conversation is about the differences between functions and random variables. The class being discussed covers topics such as set theory, probability measure, Borel sets, sigma algebra, and limsup, liminf of sets. It is mentioned that functions are not random variables unless they are defined in terms of random variables. The question is posed if there are any types of functions that are not distributions or densities for a random variable. The response is that pretty much any function can be considered a random variable, as long as it is measurable. Non-measurable functions are rare.
  • #1
zli034
107
0
There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables.

If you know functions are not random variables please please reply this post.

This class is about set theory, probability measure, Borel sets, sigma algebra, and limsup, liminf of sets.
 
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  • #2
Your question is confusing. Ordinary functions, such as polynomials, are not random variables, unless the terms themselves are.
 
  • #3
I guess the jump discontinuous functions are not random variables.
 
  • #4
As mathman indicated, functions are not random variables. If you have a random variable you can define a "function of a random variable". It you have a random variable, then the random variable has an associated function called its "distribution" and it may have an associated function that is it's "density". Talking about a "function" not being a "random variable" is like talking about a "number" not being a "plane". They are completely different concepts.

Perhaps you are tyring to ask if there are any types of functions that are not distributions or densities for a random variable?
 
  • #5
zli034 said:
There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables.

If you know functions are not random variables please please reply this post.

This class is about set theory, probability measure, Borel sets, sigma algebra, and limsup, liminf of sets.

A random variable is just a measurable function on a measure space of total measure 1.

if the sigma algebra is the Lebesque measurable sets then any continuous function is measurable. E.g. any polynomial. But pretty much any function you can think of is Lebesque measurable. Non-measurable functions are difficult to come by.
 

1. What is a random variable?

A random variable is a mathematical concept that assigns a numerical value to each possible outcome of a random event. It represents the uncertainty or randomness associated with the outcome of the event.

2. How is a function different from a random variable?

A function is a mathematical relationship between two or more variables, whereas a random variable is a numerical value that represents the outcome of a random event. Functions can take on any value, whereas random variables can only take on values associated with the event they represent.

3. Can any function be considered a random variable?

No, not all functions can be considered random variables. For a function to be a random variable, it must satisfy certain criteria, such as being able to take on a finite number of values and having a well-defined probability distribution.

4. What are some examples of functions that are not random variables?

Some examples of functions that are not random variables include trigonometric functions, exponential functions, and polynomial functions. These functions do not represent the outcome of a random event and therefore cannot be considered random variables.

5. Why is it important to understand the difference between a function and a random variable?

Understanding the difference between a function and a random variable is important because they have different mathematical properties and are used for different purposes in statistics and probability. Functions are used to describe relationships between variables, while random variables are used to model and analyze the uncertainty of random events.

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