I've been stuck on this question from my text book for a while now:

A box contains 4 dice:

  • 2 fair 4-sided dice A and B: p(i) = 1/4 i={1, 2, 3, 4}
  • 1 loaded 4-sided dice C: p(2) = 1
  • 1 loaded 4-sided dice D: p(3) = 1

You pick one of the dice at random and throw it indefinitely. The sequence of throws can be modelled as the output of the source S = S1, S2, . . .

Calculate the entropy of a symbol H(S) and the entropy rate H*(S):

I know that the entropy of a symbol can be found using the equation:

  • H(S) = lim as n goes to infinity H(Sn)

and the entropy rate:

  • H*(S) = lim as n goes to infinity of H(S1,S2,...,Sn) / n

But I am still unsure on how to proceed though I have already calculated the probability P(S1,...,Sn).


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