a)
The expected value formula is
[tex]E=\sum_ix_iP(x_i)[/tex]
Thus, in our case, after noticing that the probability of landing in a given number between 1 and 6 is equal to 1/6
[tex]\begin{gathered} E=1(\frac{1}{6})+2(\frac{1}{6})+3(\frac{1}{6})+4(\frac{1}{6})-6.5(\frac{1}{6}+\frac{1}{6}) \\ \Rightarrow E=\frac{10}{6}-\frac{13}{6} \\ \Rightarrow E=-\frac{3}{6}=-\frac{1}{2} \end{gathered}[/tex]
Thus, the answer to part a) is -0.5 dollars.
b)
An expected value of -0.5 dollars means that Hong can expect to lose 0.5 dollars per roll.
