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Chapter 4: Q.4.8 (page 253)

On May 11, 2013 at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next 48hours 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.

Short Answer

Expert verified

Mean= Expected value =-8.812

Standard deviation=11.3696

Step by step solution

01

Content Introduction

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

02

Content Explanation

Mean = Expected value

渭=SumofXP(X)

Sum of values in the fourth column of the above table

1.08-9.898=-8.812

Standarddeviation=Sumrootof(X-渭)2P(X)=127.872+1.3961=129.2686=11.36

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

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