Let X1,...,Xn be an iid sample from f(x | θ) = θxθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
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Let X1,...,Xn be an iid sample from f(x | θ) = θxθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.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 19.02Let X1, . . . , Xn be an iid sample from f(x | θ) = θxθ−1 , 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ.
- Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θEX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.Suppose θb is an unbiased point estimator for a parameter θ. We obtain 10,000 different random samples and we compute the value of θb every time. Can we say that θb will underestimate θ a total of 5000 times and it will overestimate θ another 5000 times? What do you expect to see in this experiment?
