A firm wants to bid on a contract worth \(\$ 80,000\). If it spends \(\$ 5000\) on the proposal it has a \(50-50\) chance of getting the contract. If it spends \(\$ 10,000\) on the proposal it has a \(60 \%\) chance of winning the contract. Let \(X\) denote the net revenue from the contract when the \(\$ 5000\) proposal is used and let \(Y\) denote the net revenue from the contract when the \(\$ 10,000\) proposal is used.

a. If the firm bases its choice solely on expected value, how much should it spend on the proposal?

b. Compute the variance of \(X\). 

c. Compute the variance of \(Y\).

d. How might the variance of the net revenue affect which proposal the firm chooses?

Transcribed Image Text:

X -5,000 f(x) 0.5 75,000 0.5 y f(y) -10,000 0.4 70,000 0.6