|Free Vibration |Rotating Unbalance (Harmonic Excitation) |Principal of Virtual Work | |[pic]rad/s & [pic]Hz (cps) & [pic]sec |M = mass of system‚ m = mass of unbalance mass |[pic] | |[pic] ncycle = t fn t = 1/f |Equ of Motion: [pic] |
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* Display of goods- Invitation to Treat. Pharmaceutical Society v Boots Cash Chemists. * Request for info does not create offer- Harvey v Facey [1893] 2. Offers must be communicated to the person or persons for whom it was intended. 3. Offer can be made to particular person‚ persons or whole world. – smoke balls case. 4. Offers may terminate- Revocation- Dickinson v Dodds Revocation must be communicated. * Rejection: Offeree says no. * Counter-offer: offeree makes counter
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å xi i¼1 If X‚ Y‚ and Z are independent‚ or uncorrelated‚ random variables‚ then the covariance terms are zero and: i¼1 n å xi x1 þ x2 þ Á Á Á þ xn x ¼ i¼1n ¼ n varðaX þ bY þ cZÞ ¼ a2 varðXÞ n å ðxi À xÞ ¼ 0 þ b2 varðYÞ þ c2 varðZÞ i¼1 2 3 2 å å f ðxi ; yj Þ ¼ å ½ f ðxi ; y1 Þ þ f ðxi ; y2 Þ þ f ðxi ; y3 Þ i¼1 j¼1 i¼1 ¼ f ðx1 ; y1 Þ þ f ðx1 ; y2 Þ þ f ðx1 ; y3 Þ þ f ðx2 ; y1 Þ þ f ðx2 ; y2 Þ þ f ðx2 ; y3 Þ Expected Values & Variances EðXÞ ¼ x1 f ðx1 Þ þ x2 f ðx2 Þ þ Á Á Á þ xn f
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Market Structure | NumberofSellers | TypeofProduct | BarrierstoEntry? | DemandCurve | Profit Maximization Condition | Perfect Competition | Many | Homogenous | No | Horizontal (perfectly elastic) | MR = MC | Monopoly | One | Unique | Yes | Downward Sloping | MR = MC | Monopolistic Competition | Many | Differentiated | No | Downward Sloping | MR = MC | Oligopoly | Few | Homogenous or Differentiated | Yes | Downward Sloping | MR = MC | The natural monopoly may be regulated through price‚ profit
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CH10 The government debt totaled 27% of total credit market debt although this number has risen since that time.Mortgages comprised 28%‚ Corporate and Foreign Bonds 22% and Municipal Bonds 5% of total credit market debt in the third quarter of 2008. The issuing company may choose to call the bond and require the bondholder to turn in the bond in exchange for receiving the bond’s call price. A callable bond gives the issuing company the right to call in the bond by paying the bondholder the call price
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variability Scenario 1: Demand rate < Capacity‚ and no buffer inventory Throughput rate = Demand rate Scenario 2: Demand rate > Capacity Buffer inventory builds up at rate: Demand rate – Capacity Throughput rate = Capacity rate Scenario 3: Demand rate < Capacity‚ buffer inventory exists Buffer inventory depletes at rate: Capacity – Demand rate Throughput rate = Capacity rate Throughput rate is what actually happened. Investment Analysis( National Cranberry) Capacity investment
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What proportion of a normal distribution is located in the tail beyond z = +2.00? 0.0228 What proportion of a normal distribution is located between the mean and z = 1.40? 0.4192 The Z-score corresponding to the 52nd percentile is .05 A normally distributed variable has a mean of 10 and a standard deviation of 2. The probability that a value between 7 and 9 is obtained is .2417 An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use
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error and MAD Time Series Forecasting Naïve (Just move the At value over 1 and down 1 to the Ft column) Moving Average Weighted Moving Average Exponential Smoothing Trend Adjusted Forecasting Moving Average N=3 (493+498+492)/3=494.33 Weighted Moving Average .2‚ .3‚.5 (.2*493)+(.3*498)+(.5*492)=494 Exponential Smoothing
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90%= 1.645 95% = 1.96 98% = 2.33 99% = 2.575 Hypothesis Testing *A credit card company wondered whether giving frequent flyer miles for every purchase would increase card usage‚ which has a current mean of $2500 per year. They gave free flyer miles to a simple random sample of 25 card customers and found the sample mean to be $2542 and the standard deviation to be $109. n= 25 Ho (Claim) µ=2500 OR Ha µ > 2500 *Use t-table n .50 Ha
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mk This page intentionally left blank Actuarial Mathematics for Life Contingent Risks How can actuaries best equip themselves for the products and risk structures of the future? In this new textbook‚ three leaders in actuarial science give a modern perspective on life contingencies. The book begins traditionally‚ covering actuarial models and theory‚ and emphasizing practical applications using computational techniques. The authors then develop a more contemporary outlook‚ introducing multiple
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