Hi all,
can you please help me with the following?
I have some random variable x and it distributes on {1,2,3,4} such that x = i with probability p_i.
I want to assign wights (w_1,w_2,w_3,w_3) to each result (1,2,3,4) such that the expected result: sigma(p_iw_i) will be with as maximal difference as possible from the expected result of the uniform distribution sigma(0.25w_i)
that is, given p_i, what values of w_i would yield:
sigma(p_iw_i) - sigma(0.25w_i) is maximal?
Another requirement is that sigma(w_i) = 1..
Intuitively, I think w_i = p_i (makes sense?)
can you please help me with the following?
I have some random variable x and it distributes on {1,2,3,4} such that x = i with probability p_i.
I want to assign wights (w_1,w_2,w_3,w_3) to each result (1,2,3,4) such that the expected result: sigma(p_iw_i) will be with as maximal difference as possible from the expected result of the uniform distribution sigma(0.25w_i)
that is, given p_i, what values of w_i would yield:
sigma(p_iw_i) - sigma(0.25w_i) is maximal?
Another requirement is that sigma(w_i) = 1..
Intuitively, I think w_i = p_i (makes sense?)