Question

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 $\backslash (100$. If you lose the bet, you pay$\backslash )10$. Let X = the amount of profit from a bet. Find the mean and standard deviation of X.

Short answer

Mean= Expected value $=-8.812$

Standard deviation$=11.3696$

Step-by-step solution

Content Introduction

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

Content Explanation

Mean = Expected value

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

Sum of values in the fourth column of the above table

$$\begin{gathered} 1.08-9.898 \\ =-8.812 \end{gathered}$$

$$\begin{gathered} S\tan darddeviation=Sumrootof{(X-\mu )}^{2}P\left(X\right) \\ =\sqrt{127.872+1.3961} \\ =\sqrt{129.2686} \\ =11.36 \end{gathered}$$

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.