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Probability Programming Assignment #2 Gaussian Radom Variable

Probability Programming Assignment #2 Gaussian Radom Variable. Jian -Yi Lu Visual Communications Laboratory Department of Communications Engineering, National Central University No. 300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan (R.O.C.) E-mail : j70264@hotmail.com.

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Probability Programming Assignment #2 Gaussian Radom Variable

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  1. Probability Programming Assignment #2Gaussian Radom Variable Jian-Yi Lu Visual Communications Laboratory Department of Communications Engineering, National Central University No. 300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan (R.O.C.) E-mail : j70264@hotmail.com

  2. Gaussian Radom Variable Gauss In probability theory and statistics, the normal distributionor Gaussian distribution is a continuous probability distribution that often gives a good description of data that cluster around the mean. Laplace The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian functionor bell curve.

  3. Linear Transformation fX(x) If X is N(μ ,σ), Y = aX+b, then Y is N(aμ+b,aσ) Plot X : N(μ ,σ) Plot Y : N(aμ+b,aσ) X We will provide two Gaussian data. N(8,3), you can decide the value of a,b.

  4. Mixture Gaussian Random Variable fX(x) If X1 is N(μ1,σ1) with the probability 1/3, X1 is N(-μ1,σ1) with the probability 2/3. Plot X1 Describe your findings. X We will provide two Gaussian data. N(2,3) , N(-2,3) This part is bonus. If you accomplish it, you can get additional score.

  5. Summary 1. Prove linear transform of Gaussian random variable. Mixture Gaussian Random Variable. (Bonus) Note : You need not to give me any mathematics. Just “observe” the graph and sketch your finding. Mail to: j70264@hotmail.com Submit the report + codeand packed into a zip/rar file with the file name “學號_系級_姓名”(e.g. 945003000_通訊五_林陵凌.rar) • Use whatever programming language you like. • C, C++, MATLAB, JAVA, …etc. • Due date : 2010.05.12 (Wed.) 14:50 pm • No DELAY is allowed.

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