Consider independent observations (ri, y₁), ... (rns yn), from the model Y,~ Bin(r,, p) for i = 1, ... , n, where the r, are fixed constants. Using likelihood L(p) and log-likelihood I(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To -1(p) and then s. e. (p) = √v¹. p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation. this end, estimate the Fisher Information Matrix by = == Note: To answer this question you will work by hand. Do not write in the textbox but upload a single page pdf image of your workings and results. For theoretical computations (a) to (c) you are expected to show your equations and developments in detail, simplifying as much as possible; for the numerical calculations in (d) you can use R but only write the requested results.

Consider independent observations (ri, y₁), ... (rns yn), from the model Y,~ Bin(r,, p) for i = 1, ... , n, where the r, are fixed constants. Using likelihood L(p) and log-likelihood I(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To -1(p) and then s. e. (p) = √v¹. p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation. this end, estimate the Fisher Information Matrix by = == Note: To answer this question you will work by hand. Do not write in the textbox but upload a single page pdf image of your workings and results. For theoretical computations (a) to (c) you are expected to show your equations and developments in detail, simplifying as much as possible; for the numerical calculations in (d) you can use R but only write the requested results.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

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The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
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