Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { \mathrm { m } }$

question 68

Essay

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { \mathrm { m } }$ be a random sample from a population with mean $\mu _ { 1 } \text { and variance } \sigma _ { 1 } ^ { 2 } \text {, and let } Y _ { 1 } , Y _ { 2 } , \ldots \ldots , Y _ { n }$ be a random sample with mean $\mu _ { 2 } \text { and variance } \sigma _ { 2 } ^ { 2 } \text {, }$ and that the X and Y samples are independent of one another. The expected value of $\bar { X } - \bar { Y }$ is __________ and the standard deviation of $\bar { X } - \bar { Y } \text { is }σ _ { \bar { x } - \bar { y } }$ = __________.

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Definitions:

Awareness

The state of being conscious of something, including understanding and sensitivity to certain issues.

Third-Wave Therapies

A psychological approach that incorporates mindfulness and acceptance strategies, extending beyond traditional cognitive-behavioral therapies.

Explicit Feature

A clear, direct characteristic or aspect of something that is openly shown or revealed without ambiguity.

Mindfulness

A mental practice of focusing one's awareness on the present moment while calmly acknowledging and accepting one's feelings, thoughts, and bodily sensations.