Seven successive observations on a stationary time-series are as follows:
12, 14, 13, 10, 15, 12, 15
(a) Calculate auto-covariances C0, C1, C2, C3 and C4.
(b) Calculate auto-correlation coefficients r1, r2, r3 and r4.
(c) Plot the correlogram.
________ ______ ________ ________ ______ ___ _______ ________.
______ _________ _______ ______ _______ _________ _____.
_________ ________ _____ ___ ___ _________ ________ __________ ___ ____ ________ _______.
_____ _______ _____ __________ ____.
________ ________ ___ _______ __________ _____ _______ _______ __________ ____.
__________ ________ ____ __________ __________ ___ ____ __________ ____ ______ ___.
_________ _____ _________ ___ _____ ____ __________ ___.
____ ___ ________ __________ ___ ___ ______.
________ ___ _____ __________ _____ ________ _____ _____ __________ ______.
___ _____ _________ __________ _______ ______ __________ ____ _________ ___ ___ ___.
____ _________ ____ __________ ________ ______ ___ __________ _________ ________ ______ ________.
___ ____ _________ _______ ________ ______.
_________ __________ ___ ________ ______ _________.
______ ________ _______ ________ __________ ________ ___ _______ ____.
_____ __________ __________ ________ ____ ______ _____ _________ __________ _____.
____ __________ ________ __________ ___ _____ ___ _______ __________.
________ _____ ______ ___ _________ _________ ______ ___ ______.
_________ _______ __________ _____ _____ ____ ___ __________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
In a railway marshalling yard, goods trains arrive at a rate of 36 trains per day. Assuming that the inter-arrival and service time distributions both follow exponential distribution with an average of 30 minutes, calculate the following:
(i) Traffic intensity
(ii) The mean queue length
(iii) Probability that the queue size exceeds
A company has three production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively. The transportation costs (in Rs) per unit between factories to warehouses are given in the table below:
| $D_1$ | $D_2$ | $D_3$ | $D_4$ | Capacity | |
|---|---|---|---|---|---|
| $S_1$ | 19 | 30 | 50 | 10 | 7 |
| $S_2$ | 70 | 30 | 40 | 60 | 9 |
| $S_3$ | 40 | 8 | 70 | 20 | 18 |
| Demand | 5 | 8 | 7 | 14 | 34 |
The following table represents the sales (in thousands) of mobile sets of a shop for 16 quarters over four years:
| Year | Quarter | |||
|---|---|---|---|---|
| Q_1 | Q_2 | Q_3 | Q_4 | |
| 2011 | 554 | 590 | 616 | 653 |
| 2012 | 472 | 501 | 521 | 552 |
| 2013 | 501 | 531 | 553 | 595 |
| 2014 | 403 | 448 | 460 | 480 |
A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained:$
(a) Fit a regression line taking Y as the dependent variable and X as the independent variable.
(b) Test whether the sales have any effect on revenue at 5% level of significance.
(c) Comment on the goodness of fit of the regression line.
Seven successive observations on a stationary time-series are as follows:
12, 14, 13, 10, 15, 12, 15
(a) Calculate auto-covariances C0, C1, C2, C3 and C4.
(b) Calculate auto-correlation coefficients r1, r2, r3 and r4.
(c) Plot the correlogram.
State whether the following statements are True or False. Give reasons in support of your answers.
(a) The solution of a transportation problem with 5 rows (supplies) and 4 columns (destinations) is feasible if number of possible allocations are 8.
(b) The moving averages of suitable period in a time-series are free from the influences of seasonal and cyclic variations.
(c) If the basic solutions for a system of equations are (- 2, 0, 1), (0, 1, 3), (- 2, 3, 0), then only (0, 1, 3) is feasible.
(d) In the stepwise selection method of multiple regression model, once a variable enters in the model then it always remains in the model.
(e) An enterprise requires 1000 units per month. The ordering cost is estimated to be 50 per order. The purchase price is 20 per unit and the carrying cost per unit is 10% of it. Then the economic lot size to be ordered is 775.
Using the graphical method to minimise the time required to process Job 1 and Job 2 on five machines A, B, C, D and E, find the minimum elapsed times an idle times to complete both jobs.
| Sequence | A | B | C | D | E | |
|---|---|---|---|---|---|---|
| Job 1 | Time (in hours) | 1 | 2 | 3 | 5 | 4 |
| Job 2 | Sequence | C | A | D | E | B |
| Time (in hours) | 3 | 4 | 2 | 1 | 5 |