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

In summary, the conversation is about the derivation of a red underlined term in an example and the request for help from members of a math help board. The conversation also mentions necessary reading material and questions about the meaning of a number, how the author made an equation, and how to prove something. Finally, there is a request for a computer program to verify the results in an example for specific cases.
  • #1
WMDhamnekar
MHB
376
28
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:
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  • #2
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
 
  • #3
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?
 

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

1. What is probability and how is it calculated?

Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

2. What is expected value and how is it calculated?

Expected value is the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and then summing all of these values.

3. What is a joint P.D.F. and how is it used?

A joint probability density function (P.D.F.) is a function that describes the probability of multiple random variables taking on specific values simultaneously. It is used to calculate the probability of events that involve multiple variables.

4. What are order statistics and how are they calculated?

Order statistics are the ordered values of a set of random variables. They are calculated by arranging the values in ascending or descending order and then selecting the desired value based on its position in the ordered list.

5. How are probability, expected value, joint P.D.F., and order statistics related?

Probability, expected value, joint P.D.F., and order statistics are all concepts used in probability and statistics. They are related in that they all involve the analysis and calculation of probabilities and outcomes of random events.

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