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Amy opens a new checking account and deposits $20,000 in cash at Metropolitan Bank. The

1 answer:

5 0

Answer:

i need help w this one to i’m doin it now

Explanation:

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garri49 [273]

Finding the new mean is simple: If $E[X]=10$ , then $E[2X]=2E[X]=20$ .

Meanwhile, the standard deviation is the square root of the variance, which is given by

$V[X]=E[X^2]-E[X]^2\implies V[2X]=E[(2X)^2]-E[2X]^2=4E[X^2]-(2E[X])^2$

$\implies V[2X]=4\underbrace{\left(E[X^2]-E[X]^2\right)}_{V[X]}=12$

and so the new standard deviation would be $\sqrt{V[2X]}=\sqrt{12}=2\sqrt3$ .

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