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

Question

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

Quizplus · Accepted Answer

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

Let X1,X2,……,XmX _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { \mathrm { m } }X1​,X2​,……,Xm​

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