Exercise 6.3 Hypothesis testing (all) Consider the three pmfs P and Q, and 3 given by the probability vectors p : (%, 411, i), q : (%= %= %) and 3 : (09 i! %), reSpectively. 2|: a.) Compute the symmetric error probabilities esym, 1 for hypothesis tests for all three pairs. b.) Consider the problem of ternary hypothesis testing between the three distributions, when all three have equal priors. Can you nd the minimal error probability and optimal test? C.) Cornpute D(P||Q) and D(P|IS). d.) Consider asymmetric hypothesis testing for P and S. For each 5 > 0, nd N002) E N such that nk) : 0 for all n 2 N0(e). What does that say about the limit limnaoo % log Ede)? Interpret your result in item c) in this light