Let r=0.55, c=2.1 and m=1.1. Suppose that UC and UM are not independent. What is the expected value of the point spread in the UBC game? Enter "999" if there is insufficient information to answer.

Question

Let r=0.55, c=2.1 and m=1.1.  Suppose that UC and UM are not independent. What is the expected value of the point spread in the UBC game? Enter "999" if there is insufficient information to answer.

BlackTom AI · Accepted Answer

To determine the expected value of the point spread, we would normally need a clear expression for the spread in terms of UC and UM, and the joint behavior of UC and UM.
First, note that if UC and UM were independent, there might be a straightforward way to compute E[UC ± UM] from their marginals. However, the problem states that UC and UM are not independent, which means E[UC - UM] cannot be determined from marginal expectations alone; it requires knowledge of their dependence structure (e.g., their covariance or correlation).
Second, without a specified joint distribution or a value for the covariance (or correlation) between UC and UM, any attempt to compute E[UC - UM] would be speculative. The given parameters r, c, and m do not, by themselves, provide enough information to pin down the necessary joint behavior.
Third, because the dependence is unspecified, we cannot derive a unique numerical value for the expected point spread. The correct protocol in such cases is to indicate that the information is insufficient to answer uniquely, which in this context corresponds to entering 999.
Therefore, with UC and UM not being independent and lacking the covariance or full joint specification, the problem cannot be resolved to a single numeric answer based on the information provided.
In summary, the appropriate response under these circumstances is to acknowledge the insufficiency of information to determine the expected value of the point spread, rather than producing a specific numeric result.

COMM_V 190 101-104 2025W1 Final Exam - Practice Questions - Second Half

Let r=0.55, c=2.1 and m=1.1. Suppose that UC and UM are not independent. What is the expected value of the point spread in the UBC game? Enter "999" if there is insufficient information to answer.

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