What's the PDF of a Unit Sphere Projection on the X-Axis?

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Homework Help Overview

The discussion revolves around finding the probability density function (pdf) of the projection of a unit random vector on the x-axis, where the vector is uniformly distributed over the surface of a unit sphere.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on how to approach the problem of determining the pdf related to the projection of a random vector on the x-axis. One participant suggests that the probability can be related to the area of a specific projection region compared to the total surface area of the sphere.

Discussion Status

The discussion is in the early stages, with participants exploring the relationship between area and probability in the context of the problem. Some guidance has been offered regarding the connection between the projection area and the total sphere area.

Contextual Notes

The original poster expresses uncertainty about how to begin solving the assignment question, indicating a need for foundational understanding of the concepts involved.

Micle
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Please help, I have an assignment's question but I don't idea how to work on it. The question is that:

Let R be a unit random vector points on the surface of a unit sphere. If the probability of R is uniform over the entire surface of a unit sphere, find the pdf of the projection of R on the x-axis

any idea to do so?
 
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Hi Micle

so in this example area/total sphere area is probability to find your vector within the given area

so the probability of having a projection will be related to the area area/total sphere area for a given dx incremnent at that position
 
Hi Lanedance

Thanks!
 
cheers
 

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