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

[Micle]

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?

 

[lanedance]

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

 

[Micle]

Hi Lanedance

Thanks!

 

[lanedance]

cheers