Discrete probability distributions

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Homework Help Overview

The discussion revolves around a problem involving discrete random variables, specifically focusing on the expected value and variance of a transformed variable. The original poster presents a scenario where they need to determine the value of E(X^2) given E(X-2) and VAR(X-2).

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate E(X^2) using the provided information about E(X-2) and VAR(X-2). Some participants question the calculations and suggest that the original poster may have made an error in their expansion of the expression (X-2)^2.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's approach. There is a suggestion to re-evaluate the calculations, particularly regarding the expansion of the squared term. No consensus has been reached yet.

Contextual Notes

Participants note that the original poster did not provide their detailed work, which may hinder the ability to identify specific errors. There is also an implication that the problem may involve common misunderstandings related to variance and expected values.

somecelxis
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Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?


Homework Equations





The Attempt at a Solution

 

Attachments

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somecelxis said:

Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?


Homework Equations





The Attempt at a Solution


##\text{Var}(X-2) = \text{Var}(X)## because ##\text{Var}(\cdot)## is unaffected by a non-random shift. Also: ##\text{Var}(X) = E(X^2) - (EX)^2##.
 
somecelxis said:

Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?

You made a mistake when expanding (x-2)2.

ehild
 
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Likes   Reactions: 1 person
ehild said:
somecelxis said:

Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?

You made a mistake when expanding (x-2)2.

ehild

I guess I would have caught that if the OP had typed out his work, but since I never read attached thumbnails I missed it.
 

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