caption: State (The number of toss a head first comes up)
exif: {"Image DocumentName": "State (The number of toss a head first comes up)", "Image ImageDescription": "St. Petersburg Paradox. What measure happiness? To convince you that is NOT E(W), let\u2019s consider the following famous paradox. Suppose someone offers to toss a fair coin repeatedly until it comes up heads, and to pay you  1 if this happens on the first toss,  2 if it takes two tosses to land a head,  4 if it takes three tosses,  8 if it takes four tosses, etc. What is the largest sure gain you would be willing to forgo in order to undertake a single play of this game? State (The number of toss a head first comes up) Payoff. Probability. 1st toss. 20= 1. 2nd toss. 21= 2. (\u00bd)2 = \u00bc. 3rd toss. 22= 4. (\u00bd)3 = 1/8. The table illustrates only 3 possible states, whereas theoretically, you can construct this table infinitely. The point is, the Expected wealth (i.e, E(W)) if we play this gamble is infinite if the cost of playing it is finite. Again, the expected payoff of this gamble is \u221e given finite playing cost. You may probably pay  2, or even  10 to play this gamble, depending on your risk-preference. But you would probably not pay  1,000 to play. The point is, no one on earth would pay any amount close to the expected payoff of this gamble to play. Why? Because we are not maximizing our E(W), but E(U(W)). It is really the E(U(W)) that measures our level of happiness.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}