Q6
a)We have defined the information rate distortion function as
where the minimization is over all conditional distributions 
for which the joint distribution 
satisfies the expected distortion constraint. This is a standard minimization problem of a convex function over the convex set of all 
satisfying 
for all 
and 
.
We can use the method of Lagrange multipliers to find the solution. We set up the functional
Differentiating with respect to , setting 
, we obtain
Since , we must have 
or
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