April 2012 - Question 2

[jm_kinuthia]

I am struggling to generate the number of decision functions required for this. Please assist.

Also, if possible please explain concept behind this or technique required to answer such a question as am struggling to figure it out and the notes don't explain much.

 

[suraj]

Say, Dice I is conventional dice
and Dice II is the one with three 2's and three 4's

Now we've to identify whether it's die I or II after being told the result.

Although there are 64 possible decisions functions but only 4 are meaningful, because a sane person won't say it was dice II, after seeing 1,3,5 or 6.

4 decisions functions and expected payoffs:


For calculating payoffs, say our choice was decision 1, and dice was I, so

We would win 1 if (1,3,5,6) lands with probability 4/6
win 0 if 4 lands with prob. 1/6
and, win 1 if 2 comes with prob. 1/6

So expected payoff is "5/6"
Rest try yourself

Now minimax, expected payoff and of-course common sense! , everything tells us that decision 4 is the best choice.

 

[Keshi]

This is much clearer than the examination report answer.