it's a practise question not graded Q2. Given a set of one-dimensional training samples D = {₁, 2,..., 10} as follows:X1-0.17X2X3X4X5X6 X7 X8 X9 X100.24 -0.79 0.32 0.44 0.08 0.26 0.06 -0.71 0.65(a) Suppose these data points are independently and identically sampled fromN(μ, 1). Please estimate u by maximum-likelihood estimation and furthercalculate the mean squared error (MSE) between the estimated distributionp(x)~ N(μ, 1) and the ground-truth distribution p(x) ~ N(0, 1) over thegiven training samples, i.e., (p(xi) — p(xi))².N(0, 1) and hn(b) Given the window function (u)please estimatethe probability density function (pdf) by the Parzen window method. Fur-thermore, please calculate the MSE between the estimated Parzen pdf andthe ground-truth distribution over D.(Tips: It is recommended to write computer programs to calculate the MSES.)=

Given the data as-0.170.24-0.790.320.440.080.260.06-0.710.65

Q2. Given a set of one-dimensional training samples D = {x₁, x2, ..., 10} as follows: X4 x5 x6 x7 X8 Ig X10 x2 X3 0.24 -0.79 0.32 0.44 0.08 0.26 0.06 -0.71 0.65 X1 -0.17 (a) Suppose these data points are independently and identically sampled from N(μ, 1). Please estimate u by maximum-likelihood estimation and further calculate the mean squared error (MSE) between the estimated distribution p(x) ~ N(î, 1) and the ground-truth distribution p(x) ~ N(0, 1) over the given training samples, i.e., (p(xi) – p(x;))². (b) Given the window function 4(u) ~ N(0, 1) and hn = √, please estimate the probability density function (pdf) by the Parzen window method. Fur- thermore, please calculate the MSE between the estimated Parzen pdf and the ground-truth distribution over D. (Tips: It is recommended to write computer programs to calculate the MSEs.)

Q2. Given a set of one-dimensional training samples D = {x₁, x2, ..., 10} as follows: X4 x5 x6 x7 X8 Ig X10 x2 X3 0.24 -0.79 0.32 0.44 0.08 0.26 0.06 -0.71 0.65 X1 -0.17 (a) Suppose these data points are independently and identically sampled from N(μ, 1). Please estimate u by maximum-likelihood estimation and further calculate the mean squared error (MSE) between the estimated distribution p(x) ~ N(î, 1) and the ground-truth distribution p(x) ~ N(0, 1) over the given training samples, i.e., (p(xi) – p(x;))². (b) Given the window function 4(u) ~ N(0, 1) and hn = √, please estimate the probability density function (pdf) by the Parzen window method. Fur- thermore, please calculate the MSE between the estimated Parzen pdf and the ground-truth distribution over D. (Tips: It is recommended to write computer programs to calculate the MSEs.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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