...., n,Consider independent observations (ri, y₁), ... (rn, yn), from the model Y₁ Bin(ri, p) for i = 1, ...where ther, are fixed constants. Using likelihood L(p) and log-likelihood /(p) as appropriate, compute thefollowing 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. Tothis end, estimate the Fisher Information Matrix by = -1(P) and then s. e. (p) =») = √vp=p4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and writenumerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation.

The model is for The independent observations considered are are fixed constantsThe likelihoodLog…

Answered: Consider independent observations (rı,…

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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The relationship between rainfall and the probability of flooding is given by the logistic regression p = 1 1+e-(a+br) Use the following data and regression method with a confidence level of 95% to select all true expressions about the model. r= Rainfall (mm) 200 250 280 300 325 350 380 400 p= Probability of flooding 0.02 0.09 0.12 0.3 0.4 0.7 0.9 0.93 Select one or more: O 1. The correlation of p and r is a strong negative correlation. 2. The estimation of p at r=360 is 0.78 3. The maximum error for the data happens at r=325 4. a = 10.8431 and b = -0.0337 5. R-squared=0.99
Consider independent observations (rı, y1), ... (rns yn), from the model Y, Bin(ri, 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. N 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 this end, estimate the Fisher Information Matrix by : and then s. e. ap² 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. e. (p) = √v¹¹ p=p 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…
Given the pdf: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.
Now, suppose you run an Auto Arima and you find R gives you the following model: Identify the ARIMA (p,d,q) i.e how many p terms are there? How many q terms? Coefficients: ar1 ma1 ma2 -0.7921 -0.0970 -0.3945 s.e. 0.1396 0.1802 0.1580 sigma^2 estimated as 0.1834: log likelihood=-44.07 AIC=96.14 AICc=96.68 BIC=105.61
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For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x= 6.3, y=6.0, r= -0.176, P-value = 0.221, and y = 7.30 - 0.202x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.01 significance level. The best predicted value of y when x= 4 is (Round to one decimal place as needed.)
Simplify the likelihood ratio e (µ1,..., Hr, o2) max (µ1,...,Hr,o²)EO0 e (41,...,Hr; o2) ' max (41,...,Hr,0²)EO SSTR/(r-1) SSE/(nt-r) and show that A is a decreasing function of F =
X1, X2 Xn, n volumes of random sample mean taken from the population ..... with an Exponential Distribution with a mean of 0. a) Obtain the Likelihood Function and the Log-Likelihood function of this random sample. b) Using the Log-Likelihood Function you found, obtain the Highest Likelihood Estimator MLE for the parameter 0.
Suppose X1,...,Xn are iid with PDF f(x | θ) = 2x/θ2, 0 < x < θ. (a) Write out the joint PDF f(x | θ), and write the likelihood function L(θ | x). (b) Find the MLE for θ. (c) Find the MLE for the median of the distribution.
Please help me find likelihood, log-likelihood and MLEs of two parameters, thank you.
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For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.2, y = 6.0, r=-0.209, P-value = 0.144, and y=7.48 -0.239x. Find the best predicted value of ŷ (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.05 significance level. The best predicted value of y when x = 4 is (Round to one decimal place as needed.) C

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