For part (a), you may have some mistakes. Here is what I get:
implies
so I agree that .
But,
Since , we find
So,
Then
Let's check that we have everything correct:
So, based on this, we have
I'm looking to get some insight into a moderately challenging conditional probability problem:
Consider a sequence of random variables , ..., which each take the values 0 and 1. Assume that
Pr( = 1) = 1 - Pr( = 0) = , j =1,...,n
where 0 < < 1 and that
Pr( = 1| =1) = , j = 2,...,n.
(a) Find Pr( = 0| =1), Pr( = 1| =0),Pr( = 0| =0).
(b) Find the requirements on so that this describes a valid probability distribution for , ..., .
So for part (a) I have: 1- , , and 1- , respectively.
I do not know how to begin part (b).
For part (a), you may have some mistakes. Here is what I get:
implies
so I agree that .
But,
Since , we find
So,
Then
Let's check that we have everything correct:
So, based on this, we have
Thanks for the help.
Did you have any idea on the restrictions for ?
Obviously the entire set has to be equal to a probability of 1. So are the bounds for are 0 < < 1?