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

3. If X is N(μ,σ), Y = aX+b, then Y is N(aμ+b,aσ) 1.Plot X : N(μ,σ) 2.Plot Y : N(aμ+b,aσ) We will provide two Gaussian data. N(8,3), you can decide the value of a,b. X f X (x)

4. If X 1 is N(μ 1,σ 1 ) with the probability 1/3, X 1 is N(-μ 1,σ 1 ) with the probability 2/3. 1.Plot X 1 2.Describe your findings. 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. X f X (x)

5. 1.Prove linear transform of Gaussian random variable. 2.Mixture Gaussian Random Variable. (Bonus) Note : You need not to give me any mathematics. Just “observe” the graph and sketch your finding. Use whatever programming language you like. C, C++, MATLAB, JAVA, …etc. Due date : 2010.05.12 (Wed.) 14:50 pm No DELAY is allowed. Mail to: j70264@hotmail.com Submit the report + code and 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)