Mathematics, 14.06.2021 15:50 veraanna2015
Annual windstorm losses, X and Y, in two different regions are independent, and each is uniformly distributed on the interval [0, 10]. Calculate the covariance of X and Y, given that X+ Y < 10.
Answers: 2
![Interval =[0,10]](/tpl/images/1373/7479/d9797.png)
--- i.e. the area of the shaded region
![E(XY) =\frac{1}{100} [\frac{100X^2}{2} - \frac{20X^3}{3} + \frac{X^4}{4}]|\limits^{10}_0](/tpl/images/1373/7479/7aa67.png)
![E(XY) =\frac{1}{100} ([\frac{100*10^2}{2} - \frac{20*10^3}{3} + \frac{10^4}{4}] - [\frac{100*0^2}{2} - \frac{20*0^3}{3} + \frac{0^4}{4}])](/tpl/images/1373/7479/e89e7.png)
![E(XY) =\frac{1}{100} ([\frac{10000}{2} - \frac{20000}{3} + \frac{10000}{4}] - 0)](/tpl/images/1373/7479/47cb9.png)
![E(XY) =\frac{1}{100} ([5000 - \frac{20000}{3} + 2500])](/tpl/images/1373/7479/e5ee1.png)
![E(X) =\frac{1}{50}\int\limits^{10}_0 ( [X*(10 - X)] - [X * 0])\ dX](/tpl/images/1373/7479/4acac.png)
![E(X) =\frac{1}{50}\int\limits^{10}_0 ( [X*(10 - X)]\ dX](/tpl/images/1373/7479/ff42f.png)
![E(X) =\frac{1}{50}[(5*10^2 - \frac{1}{3}*10^3)-(5*0^2 - \frac{1}{3}*0^3)]](/tpl/images/1373/7479/c60b5.png)
![E(X) =\frac{1}{50}[5*100 - \frac{1}{3}*10^3]](/tpl/images/1373/7479/fce22.png)
![E(X) =\frac{1}{50}[500 - \frac{1000}{3}]](/tpl/images/1373/7479/54c40.png)
![E(Y) =\frac{1}{50}\int\limits^{10}_0 ( [\frac{(10 - X)^2}{2}] - [\frac{(0)^2}{2}])\ dX](/tpl/images/1373/7479/d298b.png)
![E(Y) =\frac{1}{50}\int\limits^{10}_0 ( [\frac{(10 - X)^2}{2}] )\ dX](/tpl/images/1373/7479/fdada.png)
![E(Y) =\frac{1}{50}\int\limits^{10}_0 [\frac{100 - 20X + X^2}{2}] \ dX](/tpl/images/1373/7479/5fc1b.png)
![E(Y) =\frac{1}{100}\int\limits^{10}_0 [100 - 20X + X^2] \ dX](/tpl/images/1373/7479/39211.png)
![E(Y) =\frac{1}{100}( [100X - 10X^2 + \frac{1}{3}X^3]|\limits^{10}_0)](/tpl/images/1373/7479/f022f.png)
![E(Y) =\frac{1}{100}( [100*10 - 10*10^2 + \frac{1}{3}*10^3] -[100*0 - 10*0^2 + \frac{1}{3}*0^3] )](/tpl/images/1373/7479/75a34.png)
![E(Y) =\frac{1}{100}[100*10 - 10*10^2 + \frac{1}{3}*10^3]](/tpl/images/1373/7479/09243.png)
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Annual windstorm losses, X and Y, in two different regions are independent, and each is uniformly di...
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