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Exploring Gaussian Random Variables through Programming Assignments

This assignment focuses on Gaussian random variables, a key concept in probability theory and statistics. Students will analyze the normal distribution, also known as the Gaussian distribution, characterized by its bell-shaped curve. They will explore linear transformations of Gaussian variables and examine mixture Gaussian random variables. Students are required to plot the distributions and observe their behaviors without delving deeply into mathematical proofs. The assignment encourages programming in various languages, with submission due by May 12, 2010.

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Exploring Gaussian Random Variables through Programming Assignments

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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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