X₁, Instructions for Exercises 1 to 4: In each of these exercises, assume that the random variables Xn form a random sample of size n form the distribution specified in that exercise, and show that the statistic T specified in the exercise is a sufficient statistic for the parameter: Exercise 1: A normal distribution for which the mean μ is known and the variance ² is unknown; T = ₁₁ (X₁ -µ)². Exercise 2: A gamma distribution with parameters a and 3, where the value of 3 is known and the value of a is unknown (a > 0); T = I₁ X₁. Exercise 3: A uniform distribution on the interval [a, b], where the value of a is known and the value of b is unknown (b> a); T = max(X₁,..., Xn).
X₁, Instructions for Exercises 1 to 4: In each of these exercises, assume that the random variables Xn form a random sample of size n form the distribution specified in that exercise, and show that the statistic T specified in the exercise is a sufficient statistic for the parameter: Exercise 1: A normal distribution for which the mean μ is known and the variance ² is unknown; T = ₁₁ (X₁ -µ)². Exercise 2: A gamma distribution with parameters a and 3, where the value of 3 is known and the value of a is unknown (a > 0); T = I₁ X₁. Exercise 3: A uniform distribution on the interval [a, b], where the value of a is known and the value of b is unknown (b> a); T = max(X₁,..., Xn).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 31CR
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