Continuous Probability Distribution Question

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Homework Help Overview

The discussion revolves around a problem related to continuous probability distributions, specifically focusing on the relationship between random variables X and Y. Participants are exploring the conditions under which Y is less than or equal to a given value y, particularly within the interval (0, 1).

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the conditions for Y in relation to X and are questioning the implications of the range of values for Y on the corresponding values of X. There is a request for elaboration on the initial statements made regarding the relationship between the variables.

Discussion Status

The discussion is active, with participants seeking guidance on specific aspects of the problem. Some have offered insights into the relationship between the variables, suggesting that visualizing the relationship through a plot may be beneficial. However, there is no explicit consensus on the interpretations or approaches being discussed.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for discussion. The specific equations or definitions relevant to the problem have not been provided, leading to some ambiguity in the discussion.

Michael_Light
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Homework Statement



Mathematics 10.jpg



Homework Equations





The Attempt at a Solution



I can show the second one, i.e. 1/3 [sqrt(y) +1] and need help in showing the first one. Can anyone guide me?
 
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For what values of X is Y ≤ y when 0<y<1?
 
vela said:
For what values of X is Y ≤ y when 0<y<1?

Do you mind to elaborate more? I couldn't get what you mean..
 
Every value X takes on corresponds to some value of Y, so a range of values for Y corresponds to some set of values for X. If you know that 0≤Y≤y where y≤1, what do you know about the possible values of X?

It may help you to look at a plot of Y vs. X.
 

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