I. QUESTION 1 1) Show that, with the CUE for the single proposition case, the FH conditional is invariant

to updating. 2) Is the same true for the more general case? You may first want to try out the two propositions case.

3) If the answer to the above is positive, provide a proof for the general case. II. QUESTION 2 Suppose a DS theoretic BoE E[k] = {Θ, F[k], m(·)[k]}, k ≥ 0, where Θ = {H, T }, is being employed to represent the knowledge regarding a coin at instant k. Assuming that we are unaware

of the coin's bias (or the absence of bias), we can start with a vacuous BoE for E[0]. Let us now look at 25-length series of tosses (i.e., each series is of length 25).

1) With the restriction that each series has exactly 10 heads (H) and 15 tails (T ), randomly generate five 25-length series of tosses. 2 2) With the CUE parameters selected according to the proportional inertia-based strategy, for

each series of tosses, use a CUE-based update to get E[25]. 3) What observations can you make and how do you explain these observations? III. QUESTION 3 Repeat Question II but with CUE parameters selected according to the most flexible integritybased strategy.

IV. QUESTION 4 In the slides, the most flexible integrity-based parameter selection strategy has been developed

for the single proposition case. Can you generalize this strategy to the more general case to obtain all the CUE parameters? Again, you may want to try out the two propositions case.

V. QUESTION 5 In the slides, a probabilistic interpretation of the generalized version of the CUE is provided

by looking at the occurrence of an event A for which we have only β% confidence. We then assumed that we have (1 − β)% confidence about the occurrence of event A. What if we do not allocate the balance of (1 − β)% to the event A (a la DS theory)? How `

would you proceed with the probabilistic interpretation?