Question:

Assume you are the owner of TheBlues Inc., an international manufacturer of electronic products, and you are contemplating introducing a new type of Blue Ray player. After considering the potential market share for the product, your accountant estimated that after the first year of the new product on the market, TheBlues inc. may have a financial result ranging from a loss of AUD 280,000 to a profit of AUD 800,000. To take a decision in this situation, you need to assess your utility function over the expected financial outcomes.

you need to assess one of the quantiles of your utility function.

Last digit

2

Quantile index

0.25

Write in words the complete dialog to assess the uncertainty interval of the selected ?-quantile of utility, including:

Initial stage of the assessment process up till first indifference;

Elicitation of the lower bound of the ?-quantile of utility;

Elicitation of the upper bound of the ?-quantile of utility; and

Determination of the final uncertainty interval of the selected ?-quantile of

utility and its suggested point estimate.

Fourier analysis 1. Say, X1 (t) = A( 2 . t/9) x e-15 .t/71 x cos (2 n . t - Tt/) ; It| $ 5 , and zero elsewhere. Using the format of time - frequency pairs: a. Produce an educated guess (by hand) for the spectral decomposition of the signal X, (t) b. Carry on the spectral decomposition computation of X, (t) c. Compare the results in parts a and b above. d. Consider this time contamination with additive white Gaussian noise.1. Water is heated in a closed pan on a range. During the process, the water is stirred by a paddle wheel with a work amount of 900 N.m, 50 kJ of heat is transferred to the water, and 16 KJ of heat is lost to the surrounding air. Determine the final energy of the system if its initial energy is 13 kJ. Show the assumptions, the 1" law of thermodynamics, and a sketch for the problem including the energy transferred.(a) (b) (C) What are the characteristics of all heat engines? Can a heat engine to operate without rejecting any waste heat to a low-temperature reservoir? Explain. [5 marks] In a refrigerator, heat is transferred from a lower temperature medium (the refrigerated space) to a higher temperature one (the kitchen air). Is this a violation of the second law of thermodynamics? Explain. [4 marks] A heat pump is used to maintain a house at a constant temperature of 23C. The house is losing heat to the outside air through the walls and the windows at a rate of 60,000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4-000 kJ/h. (i) Draw a schematic diagram to illustrate the energy conversion taking place in the heat pump. (ii) For a COP of 2.5, determine the required power input to the heat pump. [4 + 7 marks] 2.22 Let A = 6 9 4 4 (a) Find the spectral decomposition of A as in (2.109). (b) Find the spectral decomposition of A and show that the diagonal matrix of eigenvalues is equal to the square of the matrix D found in part (a), thus illustrating (2.115). (c) Find the spectral decomposition of A- and show that the diagonal matrix of eigenvalues is equal to the inverse of the matrix D found in part (a), thus illustrating (2.116). 2.23 Find the singular value decomposition of A as in (2.117), where A NAN 2.24 If j is a vector of I's, as defined in (2. 1 1), show that the following hold