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

In summary, the conversation is about finding the pdf of the projection of a unit random vector on the x-axis, given that the probability of the vector is uniform over the surface of a unit sphere. The probability of the projection is related to the area/total sphere area for a given dx increment at a specific position.
  • #1
Micle
5
0
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 probabilty 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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  • #2
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
 
  • #3
Hi Lanedance

Thanks!
 
  • #4
cheers
 

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

What is the surface area of a unit sphere?

The surface area of a unit sphere is approximately 4π square units. This can be calculated using the formula 4πr^2, where r is the radius of the sphere (which is equal to 1 for a unit sphere).

How is the surface of a unit sphere different from other surfaces?

The surface of a unit sphere is unique because it is a perfectly symmetrical, smooth, and continuous surface. It also has a constant curvature and every point on its surface is equidistant from its center.

What is the relationship between the surface of a unit sphere and its volume?

The surface area of a unit sphere is directly proportional to its volume. This means that as the surface area increases, so does the volume. In fact, the ratio of the surface area to the volume of a unit sphere is always constant, at 3:1.

How can the surface of a unit sphere be used in real-world applications?

The surface of a unit sphere has many practical applications, such as in geography, astronomy, and physics. For example, it can be used to represent the Earth's surface in maps, or to model the orbits of planets in space.

What is the significance of the surface of a unit sphere in mathematics?

The surface of a unit sphere plays an important role in various mathematical concepts, including calculus, geometry, and topology. It is often used as a reference surface for calculating integrals and for studying the properties of curved surfaces.

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