The Textbook Derived the Following Result Show That Thisis Sthe Same As

question 22

Essay

The textbook derived the following result: $\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$
Show that thisis sthe same as $\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \beta _ { 1 } - \frac { \sigma _ { w } ^ { 2 } } { \sigma _ { w } ^ { 2 } + \sigma _ { X } ^ { 2 } } \beta _ { 1 }$

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Definitions:

Heart Rate

The number of heartbeats per unit of time, usually measured in beats per minute (bpm).

Hyperpolarized

The state of a cell membrane when its potential becomes more negative than its normal resting potential.

Sympathetic Stimulation

Activation of the sympathetic nervous system, leading to "fight or flight" responses such as increased heart rate and blood flow to muscles.

Parasympathetic Stimulation

Activation of the parasympathetic nervous system, leading to a decrease in heart rate and increase in digestive activity.