Let X, (i 1,.,n) be a random sample from the N(4,02) population with unknown ameters u and o2. Then we know that T, = E-1(X-X)²/(n – 1) is an unbiased estimator 3? and further, = 2(X- X) /n and T, = E(X-X)/(n + 1). (n-1)T ~xỉ-1. Now consider two other estimators T2 and T3 for o? where %3D at is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s.
Let X, (i 1,.,n) be a random sample from the N(4,02) population with unknown ameters u and o2. Then we know that T, = E-1(X-X)²/(n – 1) is an unbiased estimator 3? and further, = 2(X- X) /n and T, = E(X-X)/(n + 1). (n-1)T ~xỉ-1. Now consider two other estimators T2 and T3 for o? where %3D at is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s.
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.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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