what is open ended frequency distribution based on the mathematics?
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Here is a good link with an explanation (page 2)\nhttp://zaa441.tripod.com/sitebuildercontent/sitebuilderfiles/lecture8.doc\n\nBasically what it means is that the classes are open ended.\nFor example if you were looking at income this would be an example of open ended classes (the first and last)\n\nYearly Income\nBelow 20,000\n20,000-30,000\n40,000 and above
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Through the fourier map generator.
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No.  There are a lot of different types of distributions to model the many phenomena in the universe and in society.\n\nCheck out this list:\nhttp://en.wikipedia.org/wiki/Probability_distribution\nThe normal distribution is way down in the list somewhere!
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a.\nThere are few observation in X(t)\n-constant w set\n-cos and sin are periodic functions, this means cos(t) and cos(t+T) would behave identical over the time period T, 2T,3T... [consider sameargument for sin too]\n\nFor your refference let us consider the indices as n=1,2,..\n\nSo, for each n, X(t) will have a joint distribution with independent unit normal random variables Y1,Y2. And, this would be nothing but linear combination of two unit notmal distirbutions.\n\nSince, the behaviour if sine and cosine remains same over time intervals (nT), this joint distribution will remain same for all n=1,2,...\n\nThis indicated that the process {X(t)} is stationary.\n\nSince, the mean & variance of the each distribution occuring at eact time interval may not remain constant or same, This is the reason why {X(t)} is a wekly stationary process.\n\nI hope now you understand.\n\nAll the best.
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The easiest way to generate random number from a given distribution is to generate a uniform (0,1) random number; then compute the inverse cummulative probability function from that number:\nLet u be a uniform random number\nthen, x=Pinv(u,l) distributes Poisson if Pinv stands for the inverse function of the cummulative poisson distribution.\nIt's not relevant what language you use for programming
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Classes of Solutions to Mathieu's Equation\n\n  Floquet's theorem asserts that any solution to the Mathieu equation (Eq. gif) is of the form:[4,29,28]\n\n \n\nwhere is either real or imaginary and is a -periodic functiongif of . This assertion implies that solutions of Eq. gif can be separated into the product of a term of the form and a series of harmonics, , each of which is -periodic in . For values of with a non-zero imaginary component and , Eq. gif indicates that:\n\nThus, , yields an unbounded solution to the Mathieu equation. On the other hand, values of which are purely real yield bounded, oscillatory solutions for .\n\nThere are two types of bounded solutions to Mathieu's equation: functions of fractional order and functions of integral order. Functions of fractional order are obtained for . The oscillatory periods of the frequencies associated with fractional-order Mathieu functions are non-integer multiples of . The special case of corresponds to an -periodic (in terms of ) solution. These -periodic solutions are Mathieu functions of integral order.\n\nAll bounded solutions to the Mathieu equation--- those of fractional as well as integral order--- are described (in accordance with Floquet theory) by an infinite series of harmonic oscillations whose amplitudes decrease with increasing frequency:\n\n \n\nThe argument of in Eq. gif represents harmonics of frequency , while the term represents a (secular) frequency which is a function of the trap specifications (or, equivalently, of the Mathieu parameters a, q). The Mathieu parameters and also determine the coefficients , which approach zero as n increases.[36]
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b. 93,300,000 Hz\n\nFM stations measure their frequencies in Megahertz (MHz)
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Frequency = speed of light/wavelength.\n\nMake sure you keep the units straight when performing the calculations or it may not make sense.\n\nSo for your problem its (3 x 10^17 )/200 = 1.5 x 10^15 Hz
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Here's an article about it:\nhttp://en.wikipedia.org/wiki/Gaussian_elimination
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That sounds familiar... Think I'm working on it now! But I don't remember q. It is n in my book. In which case, q (if I'm thinking right) is the number of samples. Then again what's up with the ^'s? If np was > 10, then it meant that the distribution was approx. normal. You might be ahead of me right now...
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http://en.wikipedia.org/wiki/Cumulative_distribution_function
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One cool way that I have seen it derived is based on Jayne's Formalism.\n\nAssume we sample process, and measure the mean and standard devation of the samples. There are many possible distributions that will produce those exact mean and standard deviation. \n\nJayne's Formalism chooses the distribution which maximizes the entropy of the distribuiton. This is viewed mathematically as the distribution that makes the minimum number of assumptions regarding the distribution.\n\nI always thought that was kinda cool.
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Gaussian distribution
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The best way to work this out would be to plot a speed time graph for the information.\n\nOr you could express it as a simultaneous equation.
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M(t), the moment gerenating function associated to a pdf (probability distribution funciton) is given by\nm(t)=E(e^(tX))= Integral( e^(tx) f(x) dx) from -inf to + inf.\nif it exists, them m(t) is continuously diffrentiable in a neighborhood of the origin, and \nthe nth derivative of m(t), evaluated at t=0 is equal to the nth moment; that is, to E(X^n).
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Frequency = velocity of propagation / wavelength.\n\nFor light, we assume it is moving in a vacuum, so vp is 3e8 m/s.  The wavelength of 310nm is 310e-9 meters.  Then we plug the numbers in, and we get (3e8 m/s) / (310e-9 m) = 967.742e12 Hz because 1/s is the same as cycles/sec, which is a Hertz.
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If it is open on both ends, the harmonic frequencies are:\n\nf=nv/2L\n\nwhere n is the harmonic number (1st, 2nd, etc), v is the speed of sound in air (~343 m/s), and L is the length of the pipe.