# Fair G Fallacy Formula Essay

1230 Words 5 Pages
A. Calculate the expected value of the alternating St. Petersburg lottery in form of an infinite series?
Fair gamble:
In the Lottery gamble, this is chance of winning or losing for the person. A lottery is a fair gamble L=[x, -x; 1/2, 1/2\] Such that Ex=
Where, x is the random variable events.
S. No: Outcomes Prices Probability
1 H \$2 1/2=0.5
2 TH -\$4 1/4=0.25
3 TTH \$8 1/8=0.125
4 TTTH -\$16 1/16=0.0625
5 TTTTH \$32 1/32=0.03125
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N n(T…..T)H (1)^(n+1)*2^n P(x)

Expected values = 2x (1/2) + -4 x (1/4) + 8 x (1/8) + -16 x (1/16) + 32 x (1/32) + . . . . .
= 1-1+1-1+1- . . . . . =
The paradox happens on the grounds that people won't pay a boundless quantify of cash to play this
Petersburg Lottery; on the off chance that it has unbounded utility, then even a high section cost is advocated, and the danger of losing that sum is high. The most convincing samples of the normal unsatisfactory quality of danger, it seems likely that someone who didn't like to gamble would play if the prize were attractive enough.

References:
A.graham, Daniel. People.duke.edu. Accessed June 19, 2005. http://people.duke.edu/~dgraham/handouts/StPetersburgParadox.pdf.

C.cox, James. Accessed June 11, 1998. http://excen.gsu.edu/workingpapers/GSU_EXCEN_WP_2009-05.pdf.

Dehling, Herold G. Mathematics & Computing Science Groningen. Last modified November 1997. http://www.math.rug.nl/bernoulli/vorigelezingen/lezing06/inleiding06.pdf.