6. Let Y be the random variable described in Example 5.2.4, where fx(y; 0) = e(0)...

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6. Let Y be the random variable described in Example 5.2.4, where fx(y; 0) = e(0) y 0,0 > 0. Show that Ymin - is an unbiased estimator of 0. n 7. Suppose that 14, 10, 18, and 21 constitute a random sample of size 4 drawn from a uniform pdf defined over the interval [0, 0], where is unknown. a. Find an unbiased estimator for based on Y, the third order statistic. b. What numerical value does the estimator have for these particular observations? c. Is it possible that we would know that an estimate for 0 based on Y was incorrect, even if we had no idea what the true value of 0 might be? Explain. 8. A random sample of size 2,Y and Y2, is drawn from the pdf fy(y; 0) = 2y02, 0 3. Use the method of moments to estimate 0 in the pdf fy(y; 0) = (0+0) 0-1 (1-y), 0 y 1 Assume that a random sample of size n has been collected. 6. Let Y be the random variable described in Example 5.2.4, where fx(y; 0) = e(0) y 0,0 > 0. Show that Ymin - is an unbiased estimator of 0. n 7. Suppose that 14, 10, 18, and 21 constitute a random sample of size 4 drawn from a uniform pdf defined over the interval [0, 0], where is unknown. a. Find an unbiased estimator for based on Y, the third order statistic. b. What numerical value does the estimator have for these particular observations? c. Is it possible that we would know that an estimate for 0 based on Y was incorrect, even if we had no idea what the true value of 0 might be? Explain. 8. A random sample of size 2,Y and Y2, is drawn from the pdf fy(y; 0) = 2y02, 0 3. Use the method of moments to estimate 0 in the pdf fy(y; 0) = (0+0) 0-1 (1-y), 0 y 1 Assume that a random sample of size n has been collected.