Use the following information to answer questions 3 to 7. In this question, we are going practice using expectations operators in the context of a simple economic decision. Suppose an entrepreneur is deciding whether to take out a business loan from the Bank of Saskatoon. The rate at which she can borrow is a random variable, which depends on the Bank of Canada's prime rate announcement. The Bank of Canada will make the rate announcement after the entrepreneur must decide whether to take out the loan from the Bank of Saskatoon. Economic analysts have projected that there are five different rates that the Bank of Canada might announce and have assigned a probability to the likelihood of each rate. Call X the random variable that represents the rate that the Bank of Canada will announce and P(x) is the associated probability distribution function (PDF). The following is that PDF: P(x) = 10 if x = 0.005 if x= 0.015 if x = 0.016 if x =0.018 if x = 0.02 If the entrepreneur decides to borrow from the Bank of Saskatoon, she will pay a rate of X+.02. The entrepreneur needs to borrow $500, so if she borrows from the Bank of Saskatoon, the cost of borrowing is BCBsk = (X+.02)+500. Alternatively, the entrepreneur can borrow from her personal line of credit at a certain rate of .0372, and in that case the cost of borrowing would be BCLC = .0372 500. Note, that this rate does NOT depend on the Bank of Canada's announcement. So, in summary, the entrepreneur must decide between borrowing $500 at the certain rate of 0.0372 or borrowing at the uncertain rate of X+.02. Next, suppose that the entrepreneur gains utility from the net wealth from the loan and her utility function is called U (W), where Wk = 500- BC and ke {Bsk, LoC}. (Bsk refers to the Bank of Saskatoon loan and LoC refers to the line-of-credit loan). 6. Now, suppose that she has a different utility function. Suppose that her utility function is U (W)=wk.