Mathematics, 12.03.2020 18:51 blessednish86orogbi
A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 750.a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)
Answers: 2
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710](/tpl/images/0545/1849/f7cd6.png)
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3](/tpl/images/0545/1849/5ddd1.png)
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3](/tpl/images/0545/1849/f9f23.png)
![\sqrt{V[X]}=\sqrt{\dfrac{1600}3}\approx23.09](/tpl/images/0545/1849/e54a5.png)
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