ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.10 : Let D be the random outcome of rolling a dice once. A new dice has values of D* = D - 3.5. There is a total of n rolls of a dice. (a) Find the variance for D* by using the formula 6 V = [ D* (D = 1) ] [ D* (D = 1) ] + [ D* (D = 2) ] [ D* (D = 2) ] + [ D* (D = 3) ] [ D* (D = 3) ] + [ D* (D = 4) ] [ D* (D = 4) ] + [ D* (D = 5) ] [ D* (D = 5) ] + [ D* (D = 6) ] [ D* (D = 6) ]. (b) Calculate the standard deviation of D* as a square root of V. (c) Another new dice has values of D** = kD*. (i) Find the value of k so that D** has a standard deviation of 1. (ii) Find the values of D** for each outcome of D = 1, 2, 3, 4, 5 and 6, when the standard deviation is 1. (iii) Given that the average score of a dice is 3.5, find the equivalent, new and improved model of a dice, Sn in term of n and D**. (iv) Find the expected value of D** as the average of D**.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.10 : (a) 6 V = (1 - 3.5) (1 - 3.5) + (2 - 3.5) (2 - 3.5) + (3 - 3.5) (3 - 3.5) + (4 - 3.5) (4 - 3.5) + (5 - 3.5) (5 - 3.5) + (6 - 3.5) (6 - 3.5) = 17.5. V = 17.5 / 6 = 2.92. (b) Standard deviation = square root of V = (2.92) ^ (0.5) = 1.71. (c) (i) k = 1 / (standard deviation of D*) = 1 / 1.71 = 0.585. (ii) D** (D = 1) = -2.5 / 1.71 = -1.462, D** (D = 2) = -1.5 / 1.71 = -0.877, D** (D = 3) = -0.5 / 1.71 = -0.292, D** (D = 4) = 0.5 / 1.71 = 0.292, D** (D = 5) = 1.5 / 1.71 = 0.877, D** (D = 6) = 2.5 / 1.71 = 1.462. (iii) Sn = 3.5 n + 1.71 nD**. (iv) Expected value of D** = [ D** (D = 1) + D** (D = 2) + D** (D = 3) + D** (D = 4) + D** (D = 5) + D** (D = 6) ] / 6 = (- 1.462 - 0.877 - 0.292 + 0.292 + 0.877 + 1.462) / 6 = 0. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
Is This Answer Correct ? | 0 Yes | 0 No |
why should we have to maintain excess air in furnaces and boilers while burning any fuel?
How can separation of chiral chemicals affect the chemical and/or pharmaceutical industries?
How to calculate 40% of level in cylindrical vessel?
Explain what type of flow measurement devices is best for slurries?
Are there any methods of preventing cracking of carbon steel welds in refining environments?
did sulphur been a byproduct after the combustion of LPG and Natural Gas
Question 102 - (a) As an approximation, let v = Zc / 137 where v is the radial velocity for 1 s electron of an element, c is the speed of light, Z is the atomic number. For gold with Z = 79, find the radial velocity of its 1 s electron, in term of c and percentage of the speed of light. (b) As an approximation, let A x A = 1 - Z x Z / 18769 where A is the ratio of the relativistic and non-relativistic Bohr radius. Find the value of A.
Define an additive?
what is the difference between psv and prv?
how to convert Nm3/hr to Kg/hr for air, @ 10.4 kg/cm2.g dischare pressure, does density doesn't affect on calculation?
can anybody give me syallbus of chemical engineering for section engineer in railway.
MY generator water cooler inlet line height - 11 mtr inlet water line height - 7 mtr water come into the line from overhead tank, O/H tank height - 20 mtr the first tapping in the inlet line is 2" line which down to 4 mtr level plateform., second tapping in inlet water line goes to a pump 6" line installed at 4 mtr level plateform, pump capacity 200m3/hr, head- 30 mtr, hp-40. the outlet of pump of 6" water line connected to a header of 6 mtr long of 6" line, on this header the six tapping are connected, 4 nos. 3" line goes to 11 mtr height water cooler the pressure of the line is 0.15 to 0.25 kg/cm2, 2" and 4" pipe line connected to a cooler at 4 mtrlevel plateform. my question is, at 11 mtr height level the quantity of water and flow is not sufficient for my cooler, the temp. of cooler is rises much more. you are requested to suggest the modification of pipe line/ pump for take more water flow and pressure (desired pressure is 1 kg/cm2)