Variations which occur due to natural forces and operate in a regular and periodic manner over a span of less than or equal to one year are termed as cyclic variations
False, In a time series, variations which occur due ______ _________ _______ _______ _________ _______ ______.
________ _________ ________ __________ _________ __________ ____ ________ ___ _________.
______ ________ _________ _____ _______.
______ ______ _______ _____ ___ ___.
_______.
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There are three coins in a box. When tossed, one of the coins comes up heads only 30% of the time, one of the coins is fair, and the third comes up heads 80% of the time. A coin is selected at random from the box and tossed three times. If two heads and a tail come up in this order (HHT) what is the probability that the coin was the fair coin?
A hospital specialises in heart surgery. During the year 2018-19, 2000 patients were admitted for treatment. Average payment made by a patient was Rs. 120000 with a standard deviation of Rs 25000. Assuming the distribution of payments to normal, find:
i) The number of patients who paid between Rs. 1,00,000 and Rs. 1,75,000.
ii) The probability that a patient’s bill exceeds Rs. 75,000
iii) The maximum amount paid by the lowest paying one-third patient.
Obtain seasonal Indices by the “Moving average” method from the following data:
| Quarterly output of a Factory | ||||
| Year | I | II | III | IV |
| 2010 | 65 | 58 | 56 | 61 |
| 2011 | 68 | 63 | 63 | 67 |
| 2012 | 70 | 59 | 56 | 52 |
| 2013 | 60 | 55 | 51 | 58 |
A company has three production factories S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100 s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirements of 5, 8, 7 and 14 units (in 100’s) per week, respectively. The transportation costs (in rupees) per unit between factories to ware houses are given in table below.
| Warehouses/Factories | D1 | D2 | D3 | D4 | Capacity |
| S1 | 19 | 30 | 50 | 10 | 7 |
| S2 | 70 | 30 | 40 | 60 | 9 |
| S3 | 40 | 8 | 70 | 20 | 18 |
| Demand | 5 | 8 | 7 | 14 | 34 |
(a) Twenty pieces of different length of cloth contained 2, 4, 1, 3, 5, 4, 2, 7, 3, 5, 2, 2, 4, 5, 6, 4, 2, 1, 2, 4 defectsrespectively. To check the process is under control with respect to the number of defects, we should use p-chart.
(b) If density function of the time to failure of an appliance is
then reliability of the appliance for two years will be 0.444.
(c) If the probabilities are associated with the occurrence of different states of nature, then the situation is known as decision making under uncertainty.
(d) If there are 1% defectives notes of Rs.500 in a lot of 10000 notes of Rs 500, then the lot quality will be 99%.
(e) A system has four components connected in parallel configuration with reliability 0.2, 0.5, 0.4, 0.6. To improve the reliability of the system, we have to replace the weakest component to the more reliable component.
Twenty Five successive observations on a stationary time series are given as follows: 30, 33, 32, 27, 25, 28, 29, 31, 35, 34, 38, 31, 23, 24, 34, 36, 29, 32, 38, 27, 22, 29, 20, 40, 37. Calculate r1, r2, ....., r10 and plot the correlogram.
What is the average length of the queen that forms from time to time?