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2 years ago

11

How to simplify 20/10

1 answer:

Andreyy892 years ago

4 0

In order to get the answer to this question you will have to find the common factor and then divide the numerator and denominator by the common factor to get the answer.

$\frac{20}{10}$

$CF=10$

$20\div10=2$

$10\div10=1$

$\frac{2}{1} =2$

$= \frac{2}{1} or2$

Therefore the answer is "2."

Hope this helps.

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4. A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean

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Adding 2 to each value of the random variable $X$ makes a new random variable $X+2$ . Its mean would be

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The variance of a random variable $X$ is

$V[X]=E[X^2]-E[X]^2$

so the variance of $X+2$ would be

$V[X+2]=E[(X+2)^2]-E[X+2]^2$

We already know $E[X+2]=12$ , so simplifying above, we get

$V[X+2]=E[X^2+4X+4]-12^2$

$V[X+2]=E[X^2]+4E[X]+4-12^2$

$V[X+2]=(V[X]+E[X]^2)+4E[X]-140$

Standard deviation is the square root of variance, so $V[X]=3^2=9$ .

$\implies V[X+2]=(9+10^2)+4(10)-140=9$

so the standard deviation remains unchanged at 3.

NB: More generally, the variance of $aX+b$ for $a,b\in\mathbb R$ is

$V[aX+b]=a^2V[X]+b^2V[1]$

but the variance of a constant is 0. In this case, $a=1$ , so we're left with $V[X+2]=V[X]$ , as expected.

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