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 $\bar { X } - \bar { Y } \text { is }σ _ { \bar { x } - \bar { y } }$ = __________.

---

Definitions:

Prestige Drama

A genre of television or film that is produced with high quality and aimed at garnering critical acclaim, often distinguished by sophisticated storytelling and complex characters.

HBO

An American premium cable and streaming service known for original television series, movies, and documentaries.

Wes Anderson

An American filmmaker recognized for his distinctive visual and narrative style, as seen in films like "The Grand Budapest Hotel" and "Moonrise Kingdom."

Whimsical

Characterized by playful or fanciful behavior or humor, often in a way that is imaginative and unpredictable.