Suppose that you are offered the following "deal." You throw a dart at a dart board. If you hit the bullseye, you win $5. If you hit the large inner circle, you win $2. You have to pay $1 if you hit any other part of the board or you miss the board. The probability of hitting a bullseye is 10% (0.1), the probability of hitting the larger inner circle is 30% (0.3) and the probability for the rest of the board or if you miss is 60% (0.6). a. (1 pt) In words, define the random variable X b. (1 pt) List the values that X may take on x= c. (3 pts) Construct a PDF with columns for x, P(x) and x*P(x). (Hint: Do this in Excel). Bullseye inner circle Miss Totals x P(x) x* P(x) (x-) P(x) d. (1 pt) Over the long run of throwing the dart, what are your expected average winnings (u) per dart throw? = e. (1 pt) Based on numerical values, should you take your chances? Explain your decision in complete sentences.