Mathematics, 14.07.2020 02:01 kukisbae
A random variable X follows the uniform distribution with a lower limit of 720 and an upper limit of 920. a. Calculate the mean and the standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.) Mean Standard deviation b. What is the probability that X is less than 870? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Probability
Answers: 2
![E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x\,\mathrm dx=\boxed{820}](/tpl/images/0705/0539/d9cba.png)
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](/tpl/images/0705/0539/9ca41.png)
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x^2\,\mathrm dx=\frac{2,027,200}3](/tpl/images/0705/0539/86374.png)
![V[X]=\dfrac{2,027,200}3-820^2=\dfrac{10,000}3](/tpl/images/0705/0539/33e6b.png)
![SD[X]=\sqrt{V[X]}=\sqrt{\dfrac{10,000}3}\approx\boxed{57.73}](/tpl/images/0705/0539/a606b.png)
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