This is the link to the survey. It will take around 10 mins to complete. I would really appreciate it if you could take the time and complete this survey.
This survey is related to the St. Petersburg Paradox which deals with probability and decision theory. Please let me know if you have any feedback regarding this survey.
Thank you.
I was studying about expected utility from https://jonathanweisberg.org/vip/infinity-beyond.html#the-st.petersburg-paradox
Weisberg says that the paradox is not solved. What does this mean for decision theory? Should we not use expected value as a guide to decisions?
I have been beating my head against this problem for about 8 hours now and am finding conflicting answers on how to solve it. The variation of this problem I am working on is:
You toss independently a fair coin (P(head)=P(tail)=1/2) and you count the number of tosses until the 1st tail appears. If this number is n, then you receive 2^n dollars. What is the expected amount that you will receive? How much would you be willing to pay to play this game
My initial thinking was to use the expected value for a geometric random variable:
E(x) = 1/p = 1/(1/2) = 2
And then plug this value into the payout equation:
Y = 2^n = 2^2 = 4.
Thus, the expected payout using this rationalizing is $4 and one should be willing to pay no more than that to play the game. Chegg seems to agree with this logic based on several answers (last resort check after hours pulling my hair out), which is what is confusing to me since I was sure I was doing the problem wrong based off of this (Example 6.3):
https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter6.pdf
This basically says that the sum is divergent and that one should be willing to pay any amount to play the game since the more heads before tails shown, the more the payout.
Even though I worked through this problem and got $4, I felt as though that was incorrect since common sense would tell me that the more heads shown, the more I would get paid, and that even if I paid $2 per flip (which is unspecified), I would break even on the 1st (if tails was shown), and the 2nd (if heads first flip, tails on second), and the profit after the first two flips.
Can anyone help me figure out which is correct? I am leaning towards trusting a .edu site over my initial thinking and chegg, but I'm still unsure enough to ask here. Thanks!
I have always struggled to wrap my head around the meaning of an infinite expected payout in the context of the St. Petersburg paradox (http://en.wikipedia.org/wiki/St._Petersburg_paradox). I thought an experimental average payout should converge to the expected payout as more and more data points are gathered. If someone were to play the game over and over and plot their winnings, would the average payout keep going up?
Hi, I just have resolved a problem which involves the St. Petersburg Paradox, in the problem I had to compute te expected value which gives me infinite.
My problem is that given the expected value one could pay one million per game and by the previous result you eventually gain money, but I can't see why this is true, any help with the intuition.
Check out the first video from Rehan - Fire In The Belly: https://www.youtube.com/watch?v=DbM6BwKs2Lo
I thought I understood the basic principle but I can't get my head round why the expected value would be infinity? Thank you.
You toss a fair coin until you get a head. If it takes you n ο¬ips before the ο¬rst head, you get paid 2^n dollars. Let X denote the number of dollars you win. Show that E(X) = β
I don't understand how the expected value is infinity? It takes you n flips before the first head, and you get paid 2^n dollars. This means that you want as many failures as possible before getting a success (heads). Now, how is the average or expected value of this outcome infinity?
