Probability, Expected value, joint P.D.F. and order statistics

Click For Summary
SUMMARY

The discussion focuses on deriving specific mathematical terms related to order statistics and joint probability density functions (P.D.F.). The user seeks clarification on the derivation of the term represented as 2 = $n(n-1)(y-x)^{n-2}$, as well as the meaning of the constant 1 in the context of the example provided. Additionally, the user requests guidance on writing a computer program to verify results for Kth order statistics with sample sizes of n = 3 and n = 4.

PREREQUISITES
  • Understanding of order statistics in probability theory
  • Familiarity with joint probability density functions (P.D.F.)
  • Basic programming skills for statistical simulation
  • Knowledge of mathematical notation and derivations
NEXT STEPS
  • Study the concept of Kth order statistics in depth
  • Learn about joint probability density functions (P.D.F.) and their applications
  • Implement a simulation in Python or R to verify order statistics
  • Explore mathematical proofs related to expected values and their derivations
USEFUL FOR

Mathematicians, statisticians, data scientists, and students studying probability theory and order statistics.

WMDhamnekar
MHB
Messages
381
Reaction score
30
I want to know how did author derive the red underlined term in the below given Example?
Probability,Expectedvalue.png


Would any member of Math help board enlighten me in this regard?

Any math help will be accepted.
 
Last edited:
Physics news on Phys.org
Following reading material is necessary to answer my question. After reading the following material, you may answer my following questions and therby clear my doubts:
1) What is the meaning of 1 ?

2) How did author make 2 = $n(n-1)(y-x)^{n-2} ?$

3) How to prove 3 ?

Order Statistics:
1655698746147.png


Kth order statistics:

1655699729971.png

1655698794206.png


1655698865555.png
 
Write a computer program (in the language of your choice) that verifies the results in this Example for the case n = 3 and n =4 by taking large numbers of samples.

How to answer this question?
 

Similar threads

Undergrad On the expected value of a sum of a random number of r.v.s.
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What is the correct expectation value for this game with redraw?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Actual vs Expected Number of Lottery Winners
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Odds of Winning Lottery: Expected Reward & Profit
  • · Replies 8 ·
Replies
8
Views
3K
Using Multiple integrals to compute expected value
  • · Replies 16 ·
Replies
16
Views
2K
MHB Counterfactual Expectation Calculation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Interpreting Chi Squared .... backward
  • · Replies 20 ·
Replies
20
Views
4K
Graduate Neurologist: What P-values should I be expecting?
  • · Replies 19 ·
Replies
19
Views
3K
Expected value of median of rolling three fair dice
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad Probability question involving picking balls from a bag
  • · Replies 1 ·
Replies
1
Views
2K