的概率
假设X1X1X_1和X2X2X_2是具有参数ppp独立几何随机变量。什么是概率X1≥X2X1≥X2X_1 \geq X_2？ 我对这个问题感到困惑，因为除了X1X1X_1和X2X2X_2是几何图形之外，我们什么都没告诉。这不是50%50%50\%因为X1X1X_1和X2X2X_2可以在该范围内吗？ 编辑：新尝试 P(X1≥X2)=P(X1>X2)+P(X1=X2)P(X1≥X2)=P(X1>X2)+P(X1=X2)P(X1 ≥ X2) = P(X1 > X2) + P(X1 = X2) P(X1=X2)P(X1=X2)P(X1 = X2) =∑x∑x\sum_{x} (1−p)x−1p(1−p)x−1p(1−p)x−1p(1−p)x−1p(1-p)^{x-1}p(1-p)^{x-1}p =p2−pp2−p\frac{p}{2-p} P(X1>X2)P(X1>X2)P(X1 > X2) = P(X1<X2)P(X1<X2)P(X1 < X2)和P(X1<X2)+P(X1>X2)+P(X1=X2)=1P(X1<X2)+P(X1>X2)+P(X1=X2)=1P(X1 < X2) + P(X1 > X2) + P(X1 = X2) = 1 因此，P(X1>X2)P(X1>X2)P(X1 > X2) = 1−P(X1=X2)21−P(X1=X2)2\frac{1-P(X1 = X2)}{2} =1−p2−p1−p2−p\frac{1-p}{2-p}添加P(X1=X2)=p2−pP(X1=X2)=p2−pP(X1 = …