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touchhappy: ½ð±Ò+10, ¡ï¡ï¡ïºÜÓаïÖú, »Ò³£¸Ðл~~¸ú¥ϵļ¸Î»½áºÏÆðÀ´¿´£¬¸Ð¾õºÜÃ÷°×ÁËÄØ£¬Ð»Ð»£¡ 2015-05-05 14:33:58
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2Â¥2015-05-05 00:56:07
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touchhappy: ½ð±Ò+10, ¡ï¡ï¡ïºÜÓаïÖú, Thanks for your expert advice. I really appreciate the statement aforementioned "By introducing characteristic function, the Fourier transform of convolution is the product of Fourier transforms", I think I got it! 2015-05-05 14:32:49
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touchhappy: ½ð±Ò+10, ¡ï¡ï¡ïºÜÓаïÖú, Thanks for your expert advice. I really appreciate the statement aforementioned "By introducing characteristic function, the Fourier transform of convolution is the product of Fourier transforms", I think I got it! 2015-05-05 14:32:49
| Since the characteristic function is the Fourier transform of density function, we can use the beautiful properties of Fourier transform to compute the density function of the function of random variables. For example, as we know, to compute the summation function of two continuous random variables is kind of complicated. By introducing characteristic function, the Fourier transform of convolution is the product of Fourier transforms. Then by another inverse Fourier transform, we get the density function of the summation of two random variables. |

3Â¥2015-05-05 09:46:50
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4Â¥2015-05-05 10:30:29
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