解答题
21.设X，Y为随机变量，且E(X)＝1，E(Y)＝2，D(X)＝4，D(Y)＝9，ρXY＝－
【正确答案】令U＝X＋Y，则E(U)＝E(X)＋E(Y)＝3，
D(U)＝D(X＋Y)＝D(X)＋D(Y)＋2Cov(X，Y)＝4＋9＋2×(－
)×2×3＝7，
于是P{｜X＋Y－3｜≥10}＝P{｜U－E(U)｜≥10}≤
D(U)＝D(X＋Y)＝D(X)＋D(Y)＋2Cov(X，Y)＝4＋9＋2×(－
)×2×3＝7，于是P{｜X＋Y－3｜≥10}＝P{｜U－E(U)｜≥10}≤
【答案解析】