Let X1,..., X, be iid with pdff (x; A) :exp (-A|x|).Derive a likelihood ratio test of the hypothesisHo :A = X, vs HẠ:X= 1,where A1 > Ao by specifying the simplest rejection region possibleIs the test UMP against the alternative HA :1> do ?

Given information: The probability density function (p.d.f) of the random variable X is as given…

Answered: Let X1,..., X, be iid with pdf f(x; A)…

Let X1,..., X, be iid with pdf f(x; A) %3Dexp (-시피). Derive a likelihood ratio test of the hypothesis Ha:A= le Vs H.:1= .

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Two random variables X = (1,2) and Y= (-2,-1] are equiprobable and independent. Determine the correlation factor r(X,Y),
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.54 cm, y = 81.35 kg, r=0.186, P-value = 0.064, and y = - 109 + 1.12x. Find the best predicted value of ŷ (weight) given an adult male who is 180 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 180 cm tall is (Round to two decimal places as needed.) kg.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.61 cm, y = 81.52 kg, r=0.271, P-value=0.006, and y = -103 +1.18x. Find the best predicted value of ŷ (weight) given an adult male who is 155 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 193 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.59 cm, y = 81.52 kg, r= 0.416, P-value = 0.000, and y = - 102 + 1.13x. Find the best predicted value of y (weight) given an adult male who is 147 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 147 cm tall is kg. (Round to two decimal places as needed.)
7
please help
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 189 cm and weights of 37 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.50 cm, y =81.41 kg, r=0.232, P-value = 0.020, and y = - 109 + 1.17x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is kg. (Round to two decimal places as needed.)
A researcher that wanted to estimate the expectation AY of a random variable Y got three independent observations, Y, Y, Y The researcher knows the value o, of the variance of Y and is considering the following estimators: Pi = 4) Yi + (+) ¥ Py = () Yn + (;) ¥½ + () Y½ in (}) Yi + (}) ¥z + (() %D Which of the following is correct? ONone of the above Ois an unbiased estimator of l and it has the smallest variance of the three estimators. Ois an unbiased estimator of µ and it has the smallest variance of the three estimators. O and i, are both unbiased estimators of fl and Var (ſîz) < Var (îì3). is an unbiased estimator of µ and it has the smallest variance of the three estimators.
Let yit denote the outcome of a random variable for the i-th individual at time and let Xit denote a covariate measure on the i-th individual at time t, t, i = 1, ..., n, t = 1,..., T. The data could be modeled using the simple linear regression model: Yit = Bo + B₁xt + Eit, Eit~N(0, t) a) Explain why using this approach may be inappropriate. b) Write a mathematical expression of the random intercept model and the random coefficients models as alternatives to this model. c) Provide an expression for the proportion of variance attributable to each of the variance components in the random coefficients models. d) Write out an expression for the likelihood, priors and posterior for the model in part (c) e) Write out a WinBUGS code for this problem.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 192 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.80 cm, y = 81.45 kg, r=0.211, P-value = 0.035, and y = -103 +1.07x. Find the best predicted value of ŷ (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is (Round to two decimal places as needed.) kg.
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
A disk drive has a constant failure rate and an MTTF of 5000 hr. (a) What will the probability of failure be for one year of operation? (b) What will the probability of failure be for one year of operation if two of the drives are placed in active parallel and the failures are independent? (d) What will the probability of failure be for one year of operation if the system si changed to standby model. (e) Describe the effect on the MTTF with a switching failure probability of 0.05. () What would be change in MTTF if the probability of failure of standby unit is 10 percent of the failure of the primary unit in the standby mode?