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In general, the rearrangement of equation is done even if pivot element is non-zero to improve the accuracy of solution by reducing the round off errors involved in elimination process, by getting a larger determinant, which is done by finding a largest element of the row as the pivotal element.. is not important, then we may choose at each stage...
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Solve the following system of equations using Gauss-Elimination method:. What do you understand by ill-conditioned equations? Consider the following system of equations:. Solve the following system of equations by Jacobi’s iterations method:. Using Gauss-Seidel method, solve the following system of equations:. 1, –1, 1. For example, it is known that the speed v of a ship varies with the horsepower...
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2 , then the normal equations are. x y 2 = a ∑ x 3 + b ∑ x 4 9.2.6 Fitting of the Curve b. By the principle of least square, the value of S is minimum. 9.2.7 Fitting of the Curve c 0 1 y. 2 , then the normal equations are,. Find the curve of best fit...
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the following data:. Fit a least square geometric curve y = ax b to the following data:. x + to the following table of values:. a bx cx 2 in the following data:. The pressure of the gas corresponding to various volumes V is measured, given by the following data:. Fit the data to the equation pV γ = c....
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And, the equation of the line of regression of y on x is. The lines of regression of x on y and y on x are respectively x y and y x. (a) The mean of x - series;. (b) The mean of y- series;. (c) The correlation coefficient between x and y. Let the mean of x-series is x...
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10.3 COMPONENT OF TIME SERIES. The analysis of Time Series consists of the description and measurement of various changes or movements as they appear in the series during a period of time. These changes or movements are called the components of elements of time series. Fluctuations in a time series are mainly due to four basic types of variations (or...
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From (1), the required equation of the best fitted straight-line is Y = 58 + 3.4x.. Fit a straight-line trend equation by the method of least square and estimate the trend value.. Let the straight line trend equation by the method of least squares with the origin at the mid point of 1964 and 1965, and unit of x as...
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Fit a trend line to the following data by the free hand method.. Draw a trend line by semi average method using the following data.. Obtain the 5 yearly moving averages for the following series of observations.. (Rs’0000). Find the trend from the following series using a three year weighted moving average with weight 1, 2 and 1.. Trend values...
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11.4 ONE DIMENSIONAL DIAGRAM. In one dimensional diagram magnitude of the observations are represented by only one of the dimension. i.e., height (length) of the bars while the widths of the bars is arbitrary and uniform.. 11.5 TWO DIMENSIONAL DIAGRAMS. In two dimensional diagrams, the magnitude of given observations are represented by the area of the diagram. Thus the length...
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The control refers to action (or inaction) designed to change a present condition or causes it to remain unchanged. (a)Process Control: The first way for controlling the quality is process control which is concerned with controlling the quality during the process of production i.e., the control of a process during manufacture. Process control is achieved by the technique of control...
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As we have, for n = 5, A D 3 = 0, D σ control limits for x. chart are:. Range Chart: 3-σ Control Limits for R chart are:. 11.17. From mean chart we see that 2nd, 3rd, 6th and 7th samples lies outside the control limits.. Hence the process is out of control. 11.18. Since all the points with...
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Also for drawing the control chart we mark the sample No.’s along the horizontal axis and control limits and central line marked along the vertical axis. (c i ) per inspection units are marked in the c- chart.. So for computing revised control limits we omit this unit and use the remaining 15 inspection units for the purpose. The average...
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The decision rule can be summarized as: Reject H 0 if the test statistic falls in the critical region (Reject H 0 if the test statistic is more extreme than the critical value).. (1) Null Hypothesis: Set up the Null Hypothesis H 0.. (3) Level of Significance: Choose the appropriate level of significance α.. (4) Test Statistic: Compute the test...
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i.e.,there is no significant difference in the consumption of tea before and after increase of excise duty.. Conclusion: Since the calculated value of |Z| >. 2.33, both the significant values of z at 5% and 1% level of significance. Hence H 0 is rejected i.e., there is a significant decrease in the consumption of tea due to increase in excise...
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where x 1 be the mean of a sample of size n 1 from a population with mean µ 1 and variance σ 1 2.. x 2 be the mean of an independent sample of size n 2 from population with mean µ 2 and variance σ 2 2. Under the null hypothesis H 0 : µ 1 = µ...
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112.5 Since n is large, the test statistic is. 3, it is significant at all levels of significance and hence H 0 is rejected and we conclude that σ ≠ 10.. It is believed that the precision (as measured by the variance of an instrument is no more than 0.16. Write down the null and alternative hypothesis for testing this...
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Q PP b gb g b gb g b gb g b gb g. b gb gb g b gb gb g QPP. b gb gb gb g QPP. b gb gb gb g. From the following table regarding the colour of eyes of father and son test if the colour of son’s eye is associated with that of the...
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Under the null hypothesis H 0 , (i) σ x 2 = σ y 2 = σ 2 i.e., the population variances are equal or (ii) two independent estimates of the population variances are homogeneous, then the statistic F is given by. Also greater of two variances S x 2 and S y 2 is to be taken in the...
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Variable Names: Variable names (the formal term is “identifiers”) consist of letters, num- bers, and underscores. So 1/2.0 is 0.5, and 7.0/4.0 is 1.75.. Expression Statements: Most of the statements in a C program are expression statements. More generally, the syntax of an if statement is:. sub >. 1 </sub >. 2 </sub >. 3 </sub >. max is “true”...
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printf(“%f”,x1);. The root of the given equation is 1.5121.. 13.4 ALGORITHM FOR FALSE POSITION METHOD. Start of the program to compute the real root of the equation Step 2. Input the value of x 0 , x 1 and e. End of the program.. 13.5 PROGRAMMING FOR FALSE POSITION METHOD. (1) Find the Real Root of the Given Equation x...