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.
The St. Petersburg Paradox:
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
--- --- --- ---
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- . . . . . =
Why is it Paradox?
The paradox happens on the grounds that people won't pay a boundless quantify of cash to play this …show more content…
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.
K.Asae, Knut. Last modified September 1998. citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.195.3122&rep=rep1&type=pdf.
Philosophy, Standford Encyclopedia of. "The St. Petersburg Paradox (Stanford Encyclopedia of Philosophy)." Stanford Encyclopedia of Philosophy. Last modified November 4, 1998. http://plato.stanford.edu/entries/paradox-stpetersburg/.
Port, Econ. "EconPort The St. Petersburg Paradox." n.d.
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.
The St. Petersburg Paradox:
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
--- --- --- ---
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- . . . . . =
Why is it Paradox?
The paradox happens on the grounds that people won't pay a boundless quantify of cash to play this …show more content…
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.
K.Asae, Knut. Last modified September 1998. citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.195.3122&rep=rep1&type=pdf.
Philosophy, Standford Encyclopedia of. "The St. Petersburg Paradox (Stanford Encyclopedia of Philosophy)." Stanford Encyclopedia of Philosophy. Last modified November 4, 1998. http://plato.stanford.edu/entries/paradox-stpetersburg/.
Port, Econ. "EconPort The St. Petersburg Paradox." n.d.