X... Xn from distribution with pdf: f(x16) = 2x こ - OLX LO Đ>0 + (a) show that Xins is a sufficient statistic and the MLE OF O (b) show that T= X
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- The failure time (T) of an electronic circuit board follows exponentially distribution with failure rate λ = 10−4/h. What is the probability that (i) it will fail before 1000 h? (ii) it will survive at least 10,000 h ? (iii) it will fail between 1000 and 10,000 h? (iv)Determine the mean time to failure. .The Variance Inflationary Factor (VIF) measures the O standard deviation of the slope. correlation of the X variables with the Y variable. contribution of each X variable with the Y variable after all other X variables are included in the model. O correlation of the X variables with each other.Scientists need to be able to detect amounts of pollutants in the environment. Measurements were made on n 32 test specimens with a known mean concentration 2.35 ug/l of lead. It n was found that the > x; = 79.456 and > (x; – a)² = 1.0767. i=1 i=1 (a) If the population distribution of lead concentration is normal, state the minimum variance unbiased estimator of the mean. Then, compute the corresponding point estimate. Round your answer to 3 decimal places. (b) Find the estimated standard error of X. Round your answer to 3 decimal places. (c) Compute and interpret a 90% confidence interval for the true average lead concentration. (d) Did the interval you compute contain the true average? If it does not, is this a surprising result? Discuss. (e) Would you expect a wider or narrower interval if you were to compute a 95% confidence interval? Explain your answer without performing any computations.
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