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Q.4.8

Expert-verifiedFound in: Page 253

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

On May 11, 2013 at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next $48$ hours in Japan was about $1.08\%$. As in Example $4.8$, you bet that a moderate earthquake will occur in Japan during this period. If you win the bet, you win $\$100$. If you lose the bet, you pay$\$10$. Let X = the amount of profit from a bet. Find the mean and standard deviation of X.

Mean= Expected value $=-8.812$

Standard deviation $=11.3696$

To find mean and deviation of X, let us first make the following table with the given information:

Mean = Expected value

$\mu =SumofXP\left(X\right)$

Sum of values in the fourth column of the above table

$1.08-9.898\phantom{\rule{0ex}{0ex}}=-8.812$

$S\mathrm{tan}darddeviation=Sumrootof{(X-\mu )}^{2}P\left(X\right)\phantom{\rule{0ex}{0ex}}=\sqrt{127.872+1.3961}\phantom{\rule{0ex}{0ex}}=\sqrt{129.2686}\phantom{\rule{0ex}{0ex}}=11.36$

Therefore, there is an average loss of amount $\$8.81$ per bet with a standard deviation of amount $\$11.36$ in the average loss per bet in the long run.

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