Statistics and Probability Answers

define covariance of two random variables x and y and show that cov(ax + b,cy+d)

A. By adding 3 in each of the following in the set 6, 3, 5, 9, 7, 4 we obtain the set 9, 6, 8, 12, 10 and 7. Show how these 2 sets have the same standard deviations but different means.

B. After 3 months of training between these 2 employees, the proficiency test results were as follows:

Employee A: 58, 59, 60, 54, 65, 66, 52, 75, 69, 52

Employee B: 56, 87, 89, 78, 71, 73, 84, 65, 66, 48

Who do you consider more consistent? Show the statistical proof.

C. The following are the wages per hour of call center agents in a certain company:

Wages No.

P 60-61 12

P 62-63 18

P 64-65 27

P 66-67 20

P 68-69 25

P 70-71 22

P 72-73 17

P 74-75 15

P 76-77 10

Determine the following:

1. Quartile Deviations of their wages

2. Standard Deviation of their wages

B. Construct the frequency distribution of the following scores use 5 as class interval and

10 as the size of groupings. (20 points)

20 45 28 35 47 33 39

47 75 58 62 44 58 60

72 34 42 43 73 50 43

27 30 66 38 47 38 39

70 62 37 45 25 39 74

VIII. EVALUATION

Construct the following scores using frequency distribution.

88 77 72 68 66 60 55 51 47 37 26

85 77 71 68 64 58 54 50 45 36 25

81 75 71 67 63 57 53 50 45 35 24

80 75 76 67 63 57 52 49 44 33 23

79 74 70 56 62 57 52 49 40 29 19

79 74 69 66 61 56 51 48 39 27

74 64 74 46 54 64 58 66 51

76 72 62 74 72 53 64 72 50

76 66 60 35 69 40 72 38 48

45 45 33 48 55 21 32 48 66

50 55 49 40 48 47 45 54 34

Test the forecasting ability of your chosen model. For yearly data use 4 years, for quarterly data use

one year Q1 to Q4.

5.1 Present the results of your forecast using a graph and a table that has 3 columns ( Actual values,

Forecasted Values , Percentage difference)

5.2 Do a 2 year forecast for yearly data and a 1 year forecast for quarterly data for your variable and

comment on the forecast as an economic advisor on policy (NB this is now forecasting outside the data

points you have, based on the fact that you already proved in 5.1 that your model can make good

forecasts .

3.1 Describe the criteria that will be used to select the best ARIMA (p, d ,q) model

3.2 Use a table like the one in the class notes to present the estimation results for your different

models

3.3 Describe how you selected the best model that you will use for your forecast

2.5 Present the stationary graph

(1 mark)

2.6 Present the Correlogram after differencing (if you had to difference)

(1 mark)

2.7 Identify the different potential ARIMA (p, d, q) models you will use and explain how you chose

the p. the d and the q