Following is the data for number of years students studied a subject and score he/she received in that subject:
Fit the least square line to this data. What is the score of the student who has studied for two years according to this line?
To fit a least squares line to the given data, we need to find the equation of the line that minimizes the sum of the squared differences between the observed scores and the scores predicted by the line. The equation of a straight line is given by \(y = mx + b\), where \(y\) ________ ____ _______ ______ _____ _______ ________ _______ _____ _________ ___.
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The return distribution on the two securities X and Y are given in the table below:
| Possible Rates of Return | Associated Probability | |
| X | Y | Pxj=Pyj |
| 0.10 | 0.09 | 0.20 |
| 0.11 | 0.11 | 0.22 |
| 0.17 | 0.16 | 0.25 |
| 0.19 | 0.18 | 0.33 |
Find
A company has three factories F1 ,F2 F 3, and these factories supply to three markets M1 , M2 , M3 . The transportation costs from each factory to each market are given in the table. Capacities ‘ i a ’ s’ of the factories and market requirements ‘ bj ’s’ are also shown in the table. Find the minimum transportation cost.
Ships arrive at a port at the rate of one in every 4 hours, with exponential distribution of inter-arrival times. The time a ship occupies a berth for unloading has exponential distribution with an average of 10 hours. If the average delay of ships waiting for berths is to be kept below 14 hours, how many berths should be provided at the port?
A company has factories at F1 ,F2 and F3 that supply products to warehouses at W1, W2 , and W . 3 The weekly capacities of the factories are 200, 160 and 90 units, respectively. The weekly warehouse requirements are 180, 120 and 150 units, respectively. The unit shipping costs (in ₹) are as follows:
Determine the optimal distribution for this company in order to minimize its total shipping cost.
The yearly fluctuations in the groundwater table are believed to be dependent on the annual rainfall and the volume of water pumped out from the basin. The data collected on these variables for four consecutive years is given below:
Use the method of least squares to find a linear regression equation that best fits the data.
Do the stability analysis of the trivial equilibrium solution of the following competing species model:
where D1 and D2 are diffusion coefficients of the two population densities N1 and N , 2 respectively. 1 a is the growth rate, 1 b is the predation rate, 1 d is the death rate and 1 c is the conversion rate. The initial boundary conditions are
where Ni are the equilibrium solutions of the given system of equations.
“Indifference curves of an investor cannot intersect.” Is this statement true? Give reason for your answer.