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5079Choose the Greedy Backup Action 14In one state, action 1 gives immediate reward 0.8 and then moves to states of value 6 with probability 0.2 and 1 otherwise. Action 2 gives immediate reward 0.5 and then moves to states of value 2 with probability 0.5 and 3 otherwise. If gamma=0.75, which action is greedy and what backup value does it produce?机器学习中等数值题未尝试面试订阅5081Recover Epsilon From a Logged Action Probability 16An epsilon-greedy policy has 5 available actions and exactly one greedy action. A log file says the greedy action was chosen with probability 0.84. What epsilon does that imply?机器学习简单数值题未尝试面试订阅5091Discounted Cashflow 1You receive 105 in 3 years. If the annual discount rate is 0.05, what is the present value?金融与交易简单数值题未尝试面试订阅5096Continuous Discounting 1A cashflow of 100 arrives at time T=1.5. With continuously compounded rate 0.035, what is its present value?金融与交易简单数值题未尝试面试订阅5097Continuous Discounting 2A cashflow of 180 arrives at time T=2. With continuously compounded rate 0.045, what is its present value?金融与交易简单数值题未尝试面试订阅5101Level Annuity PV 1A level annuity pays 10 at each year-end for 5 years. If the discount rate is 0.04, what is the present value?金融与交易中等数值题未尝试面试订阅5111Why Earlier Cashflow MattersTwo projects pay the same total cash over three years, but one front-loads more of it. Why is its present value typically higher when discount rates are positive?金融与交易困难essay未尝试面试订阅5112Why Discount Factors Are UsefulWhy do rates desks often think in discount factors rather than only in interest rates?金融与交易困难essay未尝试面试订阅5113Compounding Convention RiskWhy can using the wrong compounding convention create pricing discrepancies even if the quoted number looks similar?金融与交易困难essay未尝试面试订阅5114Why Break-Even Rates MatterWhy is solving for an implied or break-even discount rate often more informative than reporting a present value alone?金融与交易困难essay未尝试面试订阅5115Why Long-Dated Cashflows Are SensitiveWhy does a small change in discount rate usually move the value of a far-dated cashflow more than that of a near-dated one?金融与交易困难essay未尝试面试订阅5116Coupon Bond Price 1A 3-year annual-coupon bond has face 100, coupon rate 0.05, and yield to maturity 0.04. What is its price?金融与交易中等数值题未尝试面试订阅5121Clean And Dirty Price 1A bond's annual coupon payment is 6. A buyer settles after 0.25 of the coupon period has elapsed, and the quoted clean price is 101.2. What are accrued interest and dirty price?金融与交易简单数值题未尝试面试订阅5122Clean And Dirty Price 2A bond's annual coupon payment is 4.5. A buyer settles after 0.5 of the coupon period has elapsed, and the quoted clean price is 98.8. What are accrued interest and dirty price?金融与交易简单数值题未尝试面试订阅5126Macaulay And Modified Duration 1For a 4-year annual-coupon bond with face 100, coupon rate 0.05, and yield 0.04, compute Macaulay duration and modified duration.金融与交易困难数值题未尝试面试订阅5141Flat Forward From Two Discount FactorsA curve has discount factors D(0.5)=0.992 and D(2)=0.94. If the continuously compounded forward rate is flat over the interval [0.5,2], what is that forward rate?金融与交易简单数值题未尝试面试订阅5142Longer Discount From a Flat Forward BucketThe curve has D(1)=0.97. The average continuously compounded forward rate from year 1 to year 3 is 3.5%. What is D(3)?金融与交易简单数值题未尝试面试订阅5143Average Forward Implied by Two Zero YieldsThe continuously compounded 2-year zero yield is 3.0% and the 5-year zero yield is 4.2%. What is the average continuously compounded forward rate from year 2 to year 5?金融与交易简单数值题未尝试面试订阅5144Last Half-Year Forward SliceA curve has D(1)=0.96 and D(1.5)=0.935. What is the continuously compounded forward rate over the last half-year interval [1,1.5]?金融与交易简单数值题未尝试面试订阅5145Simple Forward From Two Simple Spot RatesThe 6-month simple spot rate is 2.0% and the 18-month simple spot rate is 3.0%. What 1-year simple forward rate from 0.5y to 1.5y is implied?金融与交易简单数值题未尝试面试订阅