Let $X _ { 1 } , X _ { 2 } , \ldots , X _ { n }$

question 11

Essay

Let $X _ { 1 } , X _ { 2 } , \ldots , X _ { n }$ represent a random sample from a Rayleigh distribution with pdf $f ( x ; \theta ) = \frac { x } { \theta } e ^ { - x ^ { 2 }/ ( 2 \theta ) }\quad x > 0$
a. It can be shown that $E \left( X ^ { 2 } \right) = 2 \theta$
Use this fact to construct an unbiased estimator of $\theta$
based on $\sum x _ { i } ^ { 2 }$
(and use rules of expected value to show that it is unbiased).
b. Estimate $\theta$
from the following $n = 10$
observations on vibratory stress of a turbine blade under specified conditions:
17.08 10.43 4.79 6.86 13.88
14.43 20.07 9.60 6.71 11.15

Acknowledge the limitations and security concerns associated with electronic mail communication.

Recognize common errors in business correspondence and the limitation of software in detecting them.

Understand how to use and manage templates and common bodies of text for efficient communication.

Understand the preferences and values regarding independence and living arrangements among older Americans.

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Definitions:

Longitudinal Study

A study in which people (or animals) are followed and periodically reassessed over a period of time.

Sociobiologists

Scientists who study the biological basis of social behavior in animals and humans.

Evolutionary Concepts

Ideas and principles derived from evolutionary biology that explain the origins, development, and diversification of life on Earth, including natural selection and adaptation.

Social Behavior

Actions among individuals within a group or society, influenced by social norms, culture, and personal interactions.