All the details can be find on the picture dont reject the question =4. Given a set of two states of nature = {w₁,w₂} with prior probabilitiesP(₁) = 0.4 and P(w₂) = 0.6. Furthermore, each pattern is represented by atwo-dimensional feature vector x with Gaussian pdf p(x|w₁) ~ N(i, Σ;)(1≤ i ≤2). Specifically, we have mean vectors ₁ = (0,0)*, ₂ = (−1,2)¹ and(12)(²2).02Please answer the following questions:a) Prove that E¹ = (1(0.5) and EztΣ₂² = (-0.5b) Prove that both Σ₁ and ₂ are positive definite;c) Specify the discriminant function for each state of nature;d) Given a pattern x = (0, 2)', which state of nature should we decide on x?covariance matrices Στ=Σ2 =- (-0.5 -0.5);

Given a set of two states of nature with prior probabilities: and .

Answered: 4. Given a set of two states of nature…

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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A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. A) What are the appropriate null and alternative hypotheses to compare the means of the two groups? B) What is the appropriate test procedure for the hypotheses in Problem A? C) Carry out the test in Problem B using the criticalvalue method. D) Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke.
A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. A) Assuming this is regarded as a pilot study, how many children are needed in each group (assuming equal numbers in each group) to have a 95% chance of detecting a significant difference using a two-sided test with α = .05? B) Answer the question in Problem A if the investigators use a one-sided rather than a two-sided test. Suppose 40 children, both of whose parents smoke, and 50 children, neither of whose parents smoke, are recruited for the study. C) How much power would…
A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. Suppose 40 children, both of whose parents smoke, and50 children, neither of whose parents smoke, are recruitedfor the study.*8.37 How much power would such a study have using atwo-sided test with significance level = .05, assuming thatthe estimates of the population parameters in the pilot studyare correct?*8.38 Answer Problem 8.37 assuming a one-sided ratherthan a two-sided test is used.

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