# Question concerning the expected position of an object

Suppose there's an object within a sphere of radius $5$-metres from a given point $P=(x_0,y_0,z_0)$. The probabilities of the object being within $0-1$, $1-2$, $2-3$, $3-4$ and $4-5$ metres of $P$ are given to be respectively $p_1,p_2,p_3,p_4$ and $p_5$. With this information, is it possible to find the expected position of the object,i.e, its expected coordinates?

Stephen Tashi
You would have to make a specific assumption about the probability distribution of the object within each of those "shells".
If you assume a distribution that is spherically symmetric about (0,0,0) in each shell, the expected coordinates of the object will be (0,0,0).

What kind of an assumption do I need? Could you give an example? Also, if P = (0,0,0), how do you get the expected coordinates of the object to be (0,0,0)? Doesn't it depend on the values of the probabilities of the object being within each shell?

Stephen Tashi