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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
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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Q7. Let X; (i = 1,.,n) be a random sample from the N(u, o²) population with unknown parameters u and o?. Then we know that T, = E-1(X - X)²/(n – 1) is an unbiased estimator -xi-1 . Now consider two other estimators T, and T3 for o? where of a? and further, (n-1)T T2 = E(X – X)*/n and T3 = E(X – X)²/n + 1). %3D What is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s. Show that among the three estimators T,, T2 and T3 the one with minimum m.s.e. is T3.
Transcribed Image Text:Q7. Let X; (i = 1,.,n) be a random sample from the N(u, o²) population with unknown parameters u and o?. Then we know that T, = E-1(X - X)²/(n – 1) is an unbiased estimator -xi-1 . Now consider two other estimators T, and T3 for o? where of a? and further, (n-1)T T2 = E(X – X)*/n and T3 = E(X – X)²/n + 1). %3D What is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s. Show that among the three estimators T,, T2 and T3 the one with minimum m.s.e. is T3.
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