Mathematics, 25.09.2019 06:30 jeffrieskids13
What is the standard deviation of the random variable x "the number that comes up on the die"?
Answers: 1
giving the number that comes up follows a uniform distribution with PMF
![V[X]](/tpl/images/0260/6809/9e0b6.png)
. We have a formula for the variance in terms of the expected value, ![E[X]](/tpl/images/0260/6809/17992.png)
:![V[X]=E[X^2]-E[X]^2](/tpl/images/0260/6809/4ad5d.png)
![E[X]=\displaystyle\sum_xx\,P(X=x)=\sum_{x=1}^6\frac x6=\frac72](/tpl/images/0260/6809/b76d1.png)
![E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=\sum_{x=1}^6\frac{x^2}6=\frac{91}6](/tpl/images/0260/6809/aa7d1.png)
![V[X]=\dfrac{91}6-\left(\dfrac72\right)^2=\dfrac{35}{12}](/tpl/images/0260/6809/92380.png)
![\sqrt{V[X]}=\sqrt{\dfrac{35}{12}}\approx1.71](/tpl/images/0260/6809/aee49.png)
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What is the standard deviation of the random variable x "the number that comes up on the die"?...
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