Mathematics, 26.08.2020 17:01 maryam2863
X and Y are modeled inflation rates, in terms of %, for two different countries at the end of a five-year period. X is uniformly distributed on the interval (0, 10). Y, given X = x is uniformly distributed on the interval (0, x). Calculate Cov(X, Y).
Answers: 2
![=\frac{1}{10}\times [\log x]^{10}_{y}\\\\=\frac{1}{10}[\log 10-\log y]](/tpl/images/0729/9392/04cce.png)
![=\int\limits^{10}_{0}\int\limits^{x}_{0} {\frac{y}{10}} \, dx dy\\\\=\frac{1}{10}\times \int\limits^{10}_{0}{\frac{y^{2}}{2}}|^{x}_{0} \, dx \\\\=\frac{1}{10}\times \int\limits^{10}_{0}{\frac{x^{2}}{2}}\, dx\\\\=\frac{1}{10}\times [\frac{x^{3}}{6}]^{10}_{0}\\\\=\frac{100}{6}\\\\=\frac{50}{3}](/tpl/images/0729/9392/1c844.png)
![=\frac{50}{3}-[5\times\frac{5}{2}]\\\\=\frac{50}{3}-\frac{25}{2}\\\\=\frac{100-75}{6}\\\\=\frac{25}{6}](/tpl/images/0729/9392/dc35f.png)
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X and Y are modeled inflation rates, in terms of %, for two different countries at the end of a five...
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