Advanced Placement (AP), 25.06.2019 13:30 corcor19
Arandom variable x has a mean of 10 and a standard deviation of 3. if each value of x is multiplied by 2, what will the new mean and standard deviation be?
Answers: 1
![E[X]=10](/tpl/images/0015/8307/2082a.png)
, then ![E[2X]=2E[X]=20](/tpl/images/0015/8307/dcd7e.png)
.![V[X]=E[X^2]-E[X]^2\implies V[2X]=E[(2X)^2]-E[2X]^2=4E[X^2]-(2E[X])^2](/tpl/images/0015/8307/00a6c.png)
![\implies V[2X]=4\underbrace{\left(E[X^2]-E[X]^2\right)}_{V[X]}=12](/tpl/images/0015/8307/a14f4.png)
![\sqrt{V[2X]}=\sqrt{12}=2\sqrt3](/tpl/images/0015/8307/42d41.png)
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Arandom variable x has a mean of 10 and a standard deviation of 3. if each value of x is multiplied...
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