# Cs116 - Modelling & Simulation - Quiz #4

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2. The quiz has a total of 5 questions about Monte Carlo Simulation.
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• 1.

### Based on Practice#4 in Monte Carlo simulation, experimentation on traffic data of 500 samples with 2000 data each, what is the closest expected mean of vehicles “going straight”?

• A.

998.8

• B.

999.2

• C.

1000.3

• D.

1001.5

• E.

1002.1

C. 1000.3
Explanation
In the given question, the closest expected mean of vehicles "going straight" is 1000.3. This means that based on the Monte Carlo simulation and experimentation on traffic data, the average number of vehicles going straight is expected to be closest to 1000.3.

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• 2.

### Still based on Practice#4, experimentation on traffic data of 500 samples with 2000 data each, what is the closest expected variance of vehicles “turning right” in that intersection?

• A.

-0.05

• B.

-0.09

• C.

-0.73

• D.

0.73

• E.

0.09

C. -0.73
Explanation
The answer is -0.73 because the expected variance of vehicles "turning right" in the intersection is negative. This means that the data points are expected to be below the mean. Among the given options, -0.73 is the closest value to a negative variance.

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• 3.

### Suppose you have the sequential data that come up every time in a sequence Xt where x1=3, x2=5, x3=10, x4=6.Which of the following is correct?

• A.

The variance of the four data is 5.33

• B.

The average of the four data is 6

• C.

The variance of the first data is 10

• D.

The recursive time variance of the four data is 2.45

• E.

The variance of the first three data is 8.67

E. The variance of the first three data is 8.67
Explanation
The variance of a set of data measures the spread of the data points around the mean. To calculate the variance, we need to find the mean of the data points first. In this case, the mean of the first three data points (3, 5, 10) is (3 + 5 + 10) / 3 = 6. Then, we calculate the variance by finding the average of the squared differences between each data point and the mean. The squared differences are (3-6)^2, (5-6)^2, and (10-6)^2, which are 9, 1, and 16 respectively. The average of these squared differences is (9 + 1 + 16) / 3 = 26 / 3 ≈ 8.67. Therefore, the correct answer is that the variance of the first three data points is 8.67.

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• 4.

### Using Monte Carlo experiments of more than 1000 data in tossing a fair dice, what is the closest average of the steady state expected value?

• A.

2.7

• B.

3.5

• C.

3.9

• D.

4.1

• E.

4.25

B. 3.5
Explanation
The closest average of the steady state expected value can be determined by conducting Monte Carlo experiments with more than 1000 data points in tossing a fair dice. The steady state expected value is the average value that would be obtained over a long period of time. By performing these experiments, it is found that the closest average to the steady state expected value is 3.5.

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• 5.

### Also based from the previous question, using Monte Carlo experiments of more than 1000 data in tossing a fair dice, what is the closest variance of the steady state expected value?

• A.

1.96

• B.

2.35

• C.

2.92

• D.

3.15

• E.

3.25

C. 2.92
Explanation
Based on the previous question, where Monte Carlo experiments were conducted with more than 1000 data points in tossing a fair dice, the question is asking for the closest variance of the steady state expected value. The steady state expected value in this case refers to the average value that would be obtained after a large number of dice tosses. The closest variance to this steady state expected value is 2.92.

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