Question concerning the expected position of an object

Question

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?

Answer 1

(To be precise, let's assume that the position of the thing is uniformly distributed within the onion layers.)

Then this is a good example showing how meaningless the expected value can be. The expectation of the thing's place is the center of the sphere.

To incorporate this fact just think of a one dimensional random variable with a pdf. having two equal bumps.The expectation may be at the most improbable place.