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I think what you have described is not the correct method to estimate a 68% confidence interval in one parameter of interest. The error is in freezing the other parameter when minimising chi-squared. A better procedure to evaluate the uncertainty in parameter 1, is to evaluate the minimum chi-squared for a set of values of parameter 1, whilst allowing ...


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In the case of a 2-parameter fit, the 68% confidence space is typically an ellipse, not necessarily aligned with the axes. If you want to figure out the size of the ellipse, you should find the orientation of the ellipse, not just the intercepts of the ellipse with a horizontal and vertical line through its center. Example: fit $y=a+b x$ for a large set of ...


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The key word, to answer your question, is wavelength, as in: which wavelengths are you interested in? So far, GRBs have been seen in all wavebands, from TeV down to radio frequencies (of course, not all GRBs have been observed at all frequencies). The waveband in which GRBs release most of their energy is, unsurprisingly, that of $\gamma$ rays, with hard ...


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Yes, it is possible but it involves a lot more work. The problem is that the different components you want to separate are not similar enough for a simple subtraction to work. The frequencies are far from exactly the same, and even if they were approximately similar the relative phases would change quite fast. The phase information cannot therefore be used ...


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During the acceleration phase the object's movement can be modeled with the quadratic curve $$x=x_0 + v_0t+\frac{1}{2}at^2 \qquad\text{where } x_0 \text{ is the initial position, and }v_0 \text{ is the initial velocity}$$ During the constant velocity phase, the object's movement can be modeled with the linear equation $$x=x_1 + v_1(t-t_1)$$ where $x_1$, ...


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The average value of acceleration should just depend on the initial and final velocity and the time interval between them. Since the average value of a function over the interval a to b is the integral of the function from a to b divided by (b-a), and since the integral of acceleration gives you velocity then if the limits are $t_1$ and $t_2$ the average ...


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The measurements are repeated $N$ times for the same physical conditions; there are thus $N$ points for this single datum, which will be reported as the mean of the sample , along with the measured standard deviation. The interval is conventional, based on common usage. This makes it easier to interpret the meaning of the reported measurements. ...



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