Mathematics, 11.07.2019 13:50 mariap3504
Agas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. the total of gas pumped at the station in a month is a random variable y (measured in 10,000 gallons) with a probability density function (p. d.f.) given by compute e(y)
Answers: 1
![F(\infty)= \int\limits^{\infty}_{-\infty} {f(y)} \, dy=1 \\ \\ \Rightarrow \int\limits^1_0 {cy} \, dy +\int\limits^2_1 {(2-y)} \, dy=1 \\ \\ \Rightarrow \left. \frac{cy^2}{2} \right]^1_0+\left[2y- \frac{y^2}{2} \right]^2_1=1 \\ \\ \Rightarrow \frac{c}{2} +4-2-2+ \frac{1}{2} =1 \\ \\ \Rightarrow \frac{c}{2} = \frac{1}{2} \\ \\ \Rightarrow \bold{c=1}](/tpl/images/0077/2939/a163f.png)
![E(y)=\int\limits^{\infty}_{-\infty} {yf(y)} \, dy \\ \\ =\int\limits^1_0 {y^2} \, dy +\int\limits^2_1 {(2y-y^2)} \, dy \\ \\ =\left. \frac{y^3}{3} \right]^1_0+\left[y^2- \frac{y^3}{3} \right]^2_1 \\ \\ = \frac{1}{3} +4- \frac{8}{3} -1+ \frac{1}{3} \\ \\ =1](/tpl/images/0077/2939/8c238.png)
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Agas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. the...
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