Deterministic versus Probabilistic Model

Posted: August 25th, 2021

Hamoud Midterm

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Hamoud midterm

Question 1: Deterministic versus Probabilistic Model

The deterministic model refers to a mathematical model whose purpose is to give a single solution when describing the results of an ‘experiment’ following the right input. On the other hand, the probabilistic model has established yield distribution of different possible results from an ‘experiment’ given specific inputs. Mainly, the model describes all possible outcomes while giving the likelihood of the occurrence of each outcome.

Question 2: Garbage in, Garbage Out (GIGO)

The GIGO concept is commonly associated with computers and mathematics. The concept implies that the type of input that is fed into a system determines the quality of output that the model or system will yield. Thus, improperly stating a mathematical model eventually yielding wrong results. Further, when the right model is fed with wrong figures, it would give the wrong information.

Question 3: Break-even Calculations

1. Break-even point (in units) = Fixed costs/ (Price – variable costs)

Fixed costs

• Cost of renting = $300 per 3 hours
• Tutor’s wage = $25 per hour*3 = $75 per 3 hours

Total costs = $375 per 3 hours

Price

• Session charges = $20 per student, * 3 sessions = $60 per session

Variable costs

• Production cost = $5 per student *3 sessions = $15 per session

Therefore, break-even enrollment units = $375/$(60-15) = 8 students per session.

• For reduced fixed costs;

Break-even point = $275/ $(60-15) = 6 students per session. Hence, reducing rental costs to $200 per three hours lowers the break-even number of attendances.

Question 4

1. Probability of failure, for series panelp_f = g (F_R1-6) = 0.10*0.10*0.15*0.15*0.15*0.08 = 0.0000027 or 2.7 x 10⁶

Parallel system, p_f = 1 – g(F_R2-3) = 0.99

Probability that the system fails = 0.99*2.7 x 10⁶ = 2.6 x 10⁶

• Probability that system works properly
• Probability of failure = 0.999

Question 5

1. Reversed probability

P(F|D=0) = 0.9      P(F|D=1) =0.8             P(F|D=0) = 0.7            P(8F|D=3) =0.4

P(U|D=0) = 0.2     P(U|D=1) = 0.7           P(U|D=2) = 0.9           P(F|D=3) = 0.6

• Payoff value for each combination

P (F/U|D = 0) = 0.9*0.2 = 0.18, P (F/U|D = 1) =0.8*0.7 = 0.56, P (F/U|D =0, 2) = 0.7*0.9 = 0.63, P (F/U|D = 3) = 0.4*0.6 = 0.24

• Decision tree

Customers’ Attitude

P (F=favorable)

P(U=unfavorable)

P (N=no opinion)

Probabilities

P(F|D=0) = 0.9

P(F|D=1) =0.8

P(F|D=0) = 0.7

P(F|D=0) = 0.7

P(U|D=0) = 0.1

P(U|D=1) =0.2

P(U|D=0) = 0.3

P(U|D=0) = 0.3

P(N|D=0) = 0.2

P(N|D=1) =0.9

P(N|D=0) = 0.9

P(N|D=0) = 0.6

Payoffs

0.9*0.4+0.8*0.3+0.7*0.2+0.7*0.1 = 0.81

0.1*0.4+0.2*0.3+0.3*0.2+0.1*0.3 = 0.19

0.2*0.4+0.3*0.9+0.2*0.9+0.1*0.6 = 0.59

• Expected Monetary Value (EMV)

To calculate EMV, the formula used is as follows;

EMV = probability x impact, in this case, thee impact is the payoffs attributed to each decision. Hence, EMV is; 0.81*4= 3.24=> favorable, 0.19*3=0.57 => unfavorable, 0.59*1=0.59 for no opinion.

The highest earned value is 3.24. The figure represents the highest returns of the undertaken decision.  Hence, favorable is the best decision that should be made. The results imply that the product has a positive attitude from the customers.

• EMV of sample information = 0.81*0.19*0.59 = 0.09081. Hence, there is a 9.081% chance that the survey would be conducted to obtain the required information about the attitude of the customer over the impending introduction of the product into the target market.