Finite expectation value <-> finite sum over Probabilties

In summary, if X is a real valued random variable with finite E[|X|], then the sum of P(|X|>n) for all natural numbers from 1 to infinity is also finite. This can be related to the formula for E[|X|], which is the sum of |x|*P(|x|) for all values of x.
  • #1
Mr.Brown
67
0

Homework Statement


If X is a real valued random variable with E[|X|] finite. <-> [tex]\sum(P(|X|>n))[/tex] finite

, with the sum over all natural numbers from 1 to infinity.

Homework Equations



As a tip I am given that for all integer valued X>0 E(X) = [tex]\sum(P(X)>k[/tex] , where the sum goes over all k =1 to k=infinity (k is a natural number)

The Attempt at a Solution



I don´t really have an idea i tried to find a way to relate integer valued stuff to real valued stuff by summing over all real valued stuff that are not integer.
But don't get anywhere :(
Hope for some advice
 
Physics news on Phys.org
  • #2
What is the formula for E[|X|]?
 
  • #3
It´s just the expectation value E[|X|]= sum over all |x|*P(|x|).
 
  • #4
ok solved it :)
 

1. What is the concept of finite expectation value?

The finite expectation value, also known as the mean or average, is a mathematical concept used to describe the central tendency of a set of data. It is calculated by taking the sum of all values in the data set and dividing by the number of values in the set.

2. How is finite expectation value related to probability?

The finite expectation value is closely related to the concept of probability. In probability theory, the expectation value of a random variable is the long-term average of its possible values, weighted by their probabilities. This means that the finite expectation value can be seen as the average outcome of a random event over a large number of trials.

3. Can the finite expectation value be negative?

Yes, the finite expectation value can be negative. It is simply a mathematical calculation and can result in a negative value if the data set contains a mix of positive and negative numbers. However, in certain contexts, a negative expectation value may not make sense and can be interpreted as an indicator of an error in the data or calculation.

4. What is the significance of a finite expectation value?

The finite expectation value is an important measure in statistics and probability theory. It provides a way to summarize a large set of data and make predictions about future outcomes. It is also used in decision-making processes and risk analysis, as it can help determine the likelihood of certain events occurring.

5. How is the finite expectation value calculated?

The finite expectation value is calculated by taking the sum of all values in a data set and dividing by the number of values in the set. This can be represented mathematically as E(X) = (x1 + x2 + ... + xn) / n, where X is the random variable and x1, x2, ..., xn are the individual values in the data set. This calculation assumes that each value in the data set has an equal probability of occurring.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
604
  • Calculus and Beyond Homework Help
Replies
13
Views
11K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
455
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
638
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
872
Back
Top