Consider the following two-dimensional data sampled from two categories, denotes Gg. Each ofthem comes from a Gaussian density p(x\Cx) ~ N(Hx, Ek):C2Sample 13.01.71.1.1-1.31.23.50.23.53.1.55.01.54.340.64.53.20.80.54.04.02.7a. Find the unbiased maximum-likelihood estimation of µ and Ex for each class of the givendata.b. Generate 10 data points for each class from your estimated density.c. Generate a third class C3 of data which contains 10 data points with the same covariance E,as C1, and a different mean.

In this problem, we are given a dataset with two-dimensional samples from two categories, C1 and C2,…

Answered: Consider the following two-dimensional…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Exercise 1. Suppose that X ~ N(7, 2.25). Data x is an observed IID sample of size n = 500 from the distribution of X. That is, the IID Data Model is: x + X, where X - IID(500) X IID(500) N(7,2.25). (a) Give a rough sketch of your guess at the density histogram of data x, including labeled tick marks on the horizontal axis. Explain why you expect the density histogram of the data x to look this way. (b) The sample mean x and the sample variance s2 of these 500 data values were computed. What would you guess their values are and why? (c) How many (give a count, not a percentage) of the 500 data values in x would you guess are less than 6? Explain why you believe your guess should be reasonable.
Consider the paired data: I 1.42 y 4.11 4.22 12.28 9.16 28.62 7.92 24.82 9.59 29.82 Eį Find estimates for the linear model y = Bo+812, +e, where ~ N(0,0²). That is find 3o. 31, à. Also perform a test of the null hypothesis Ho 3₁ = 0 at level a = 0.01.
You obtained the following raw data when setting up a Biuret standard curve: BSA (mg/ml) Absorbancy 540nm 0 0.158 1 0.210 2 0.260 3 0.305 4 0.360 5 0.410 6 0.455 7 0.510 8 0.530 9 0.550 10 0.554 What would the quality of the line-fit (R2 value) be if you do not exclude experimental outliers? (Give you answer to 4 decimal places)
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range: 415 420 422 423 426 429 432 435 436 439 446 447 448 452 459 463 464 (a) Construct a boxplot of the data. 420 430 440 450 460 420 430 440 450 460 420 430 440 450 460 420 430 440 450 460 Comment on any interesting features. (Select all that apply.) There are no outliers. There is little or no skew. There is one outlien The data is strongly skewed. The data appears to be centered near 439. The data appears to be centered near 429. (b) Is it plausible that the given sample observations were selected from a normal distribution? O Yes ○ No (c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) Does the interval suggest that 445 is a plausible value for true average degree of polymerization? O Yes ○ No Does the interval suggest that 451 is a…
Consider a random sample X1,..., X, with n > 3 from the exponential distribution with parameter A > 0 and density 1 f(x; A) = e/A I> 0. Consider the following two estimators of A: 3 Ex,, X =nX1). = i=1
There are two Gaussian curves below (Plots A and B), along with the respective R source codes.Looking at the plots and the source codes provided, identify the parameters of respective Gaussian pdf's (probability density functions) and the numeric value of x in the PDF F(x)express the areas under the curves in terms of F(x). ( Do not calculate those areas.Your answers must be like F(x) or 1- F(x) for a relevant value of x.) Below is the source code and image for part B
only d
For the data set shown below, complete parts (a) through (d) below. x| 20 30 40 50 60- y 102 95 93 81 68 Se -U (Round to four decimal places as needed.) (c) Assuming the residuals are normally distributed, use technology to determine sp. - (Round to four decimal places as needed.) (d) Assuming the residuals are normally distributed, test Ho: B, = 0 versus H,: ß, #0 at the a = 0.05 level of significance. Use the P- Determine the P-value for this hypothesis test. P-value = (Round to three decimal places as needed.) Which of the following conclusions is correct? O A. Do not reject Ho and conclude that a linear relation does not exist between x and y. O B. Reject H, and conclude that a linear relation does not exist between x and y. O C. Reject Ho and conclude that a linear relation exists between x and y. O D. Do not reject H, and conclude that a linear relation exists between x and y.
Two high school seniors find themselves with much time and nothing to do. They decide to devise a computer game in which a cursor moves randomly along the x axis between -2 and 2. The game they play is to stop the cursor at random points between -2 and 2 without looking at the screen. Such a game results in a uniform distribution overthe interval between -2 and 2 and resemebles a density curve. The height of the density curve is:
The following table represents the data collected for tree volume (in cm³ ) and diameter-at- breast height (in cm) for sugar maple trees. Tree volume can be predicted by using Dbh. 197 175 | Tree volume (cm ³ 159 Dbh (cm) 163 159 188 170 22.0 25.2 19.8 30.2 22.8 25.8 26.4 The summaries of the data are as follows: Σχ-172.2 ΣΥ- 1211 ΣΧΥ-29995.6 Σχ4305.56 ΣΥ= 210809 (i) Calculate the rank correlation coefficient and comment on your finding. (ii) Find the least squares regression line of Y = a + bX. Hence interpret the value of the regression coefficient "b". Estimate the tree volume when the dbh is 50 cm. Comment on the reliability of the estimate. (iii)
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range: 415 420 421 422 426 427 432 434 437 438 446 447 450 452 457 463 464 (a) Construct a boxplot of the data. 420 430 440 450 460 420 430 440 450 420 430 440 450 460 420 430 440 450 460 Comment on any interesting features. (Select all that apply.) There is one outlier. n The data is strongly skewed. n The data appears to be centered near 428. n There are no outliers. n The data appears to be centered near 438. n There is little or no skew. (b) Is it plausible that the given sample observations were selected from a normal distribution? Yes o No (c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) Does the interval suggest that 440 is a plausible value for true average degree of polymerization? o Yes o No Does the interval suggest that 456 is a…
In a certain type of metal test specimen, the normal stress on a specimen is known to be functionally related to the shear resistance. The following is a set of coded experimental data on the two variables: Normal Stress, x Shear Resistance, y 26.8 25.4 28.9 23.6 27.7 23.9 24.7 28.1 26.9 27.4 22.6 25.6 26.5 27.3 24.2 27.1 23.6 25.9 26.3 22.5 21.7 21.4 25.8 24.9 Estimate the B1.

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