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Sma2110:Real Analysis Ii Question Paper

Sma2110:Real Analysis Ii

Course:Bachelor Of Computer Science

Institution: Meru University Of Science And Technology question papers

Exam Year:2013

QUESTION ONE – (30 MARKS)
(a) Draw the trend by semi-average method for the following data. (6 Marks) Year Values 1988 61.5 1989 70.1 1990 68.4 1991 72.4 1992 84.6 1993 91.4 1994 98.6 1995 100.8 1996 115.2
(b) Explain the following terms: (i) Sinusoid (2 Marks) (ii) Time series (2 Marks) (iii) Autoregressive process (2 Marks)
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(c) The following is the analysis of electricity consumption of heating for various maximum daily temperatures. The recorded data over a period of five random days are as shown below
Day Maximum Temperatures(0C) Electricity Consumption (‘000’ units)
1 26 35 2 31 20 3 25 37 4 26 24 5 14 42
Find the least squares regression line of electricity consumption on maximum temperature. (6 Marks) (d) Calculate trend values using moving average centering for the following data. (6 Marks) Quarter Original data (y) Year 1 1 2.2 2 5.0 3 7.9 4 3.2 Year 2 1 2.9 2 5.2 3 8.2 4 3.8 Year 3 1 3.2 2 5.8 3 9.1 4 4.1 (e) Explain the two types of time series data. (4 Marks) (f) Give two examples of time series. (2 Marks)
QUESTION TWO – (20 MARKS)
(a) The data below relates the weekly maintenance cost (sh) to the age (in months) of ten machines of similar type in a manufacturing company. Find the least squares regression line of maintenance cost on age and use this to predict the maintenance cost for machine of this type which is 40 months old. (12 Marks) Machine 1 2 3 4 5 6 7 8 9 10 Age (x) 5 10 15 20 30 30 30 50 50 60 Cost (y) 190 240 250 300 310 335 300 300 350 395
3
(b) Explain the following components of time series (i) Secular trend (2 Marks) (ii) Cyclical trend (2 Marks) (iii) Irregular variation (2 Marks) (iv) Seasonal variation (2 Marks)
QUESTION THREE – (20 MARKS)
(a) Assuming a four year cycle, calculate the trend by moving average from the following data. (4 Marks)
t Year Production 1 1961 515 2 1962 518 3 1963 467 4 1964 502 5 1965 546 6 1966 557 7 1967 571 8 1968 586 9 1969 464 10 1970 612
(b) State three merits and three demerits of moving averages. (6 Marks) (c) Explain the following terms: (i) Correlogram (2 Marks) (ii) Period gram (2 Marks) (iii) Auto regressive model (2 Marks) (d) Outline four importance of time series. (4 Marks)
QUESTION FOUR – (20 MARKS) (a) Consider an (2) process given by = 1 1 2
2 + . Is the process stationary? If so obtain its autocorrelation function. (14 Marks)
4
(b) Calculate the seasonal figures using the additive model. (6 Marks) y t Year 1 Quarter 1 20 23 2 15 29 3 60 34 4 30 39 Year 2 Quarter 1 35 45 2 25 50 3 100 55 4 50 61

Sma2110:Real Analysis Ii Question Paper

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