Provide an Appropriate Response $f ( x ) = \frac { 1 } { \sqrt { 2 \pi } } e ^ { - x ^ { 2 } / 2 }$

question 227

Essay

Provide an appropriate response.
-The standard normal probability density function is defined by $f ( x ) = \frac { 1 } { \sqrt { 2 \pi } } e ^ { - x ^ { 2 } / 2 }$ .
(a) Use the fact that $\int _ { - \infty } ^ { \infty } \frac { 1 } { \sqrt { 2 \pi } } e ^ { - } x ^ { 2 } / 2 d x = 1$ to show that $\int _ { 0 } ^ { \infty } \frac { 1 } { \sqrt { 2 \pi } } x ^ { 2 } e ^ { - x ^ { 2 } / 2 } \mathrm { dx } = \frac { 1 } { 2 }$ .
(b) Use the result in part (a) to show that the standard normal probability density function has variance $1 .$

Recognize the symptoms and brain areas associated with specific neurological disorders (e.g., agnosia, speech comprehension difficulties).

Comprehend the role and function of the motor and sensory cortices.

Understand the principles of lateralization and hemispheric specialization.

Describe the neurological basis of language and speech.

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Definitions:

Lapse

A temporary failure to maintain a higher state of wellness or achievement, often seen as a brief return to previous unhealthy behaviors.

High-Risk Situation

Circumstances or environments that have an increased likelihood of leading to negative or undesired outcomes.

High-Risk Situations

Situations that have a higher probability of leading to undesired outcomes or dangers.

Unhealthy Behaviors

Actions or habits that negatively affect an individual’s physical or mental health, such as smoking or excessive drinking.