2025考研數(shù)學(xué)（一）概率論專項(xiàng)卷姓名：______班級：______學(xué)號：______得分：______第一部分：單選題（共8題，每題5分，共40分）1.設(shè)A、B為兩個隨機(jī)事件，且P(A)=0.6，P(B)=0.4，P(A∪B)=0.8，則P(A∩B)=A.0.2B.0.3C.0.4D.0.52.設(shè)隨機(jī)變量X服從參數(shù)為λ的泊松分布，且E(X)=2，則D(X)=A.1B.2C.3D.43.設(shè)隨機(jī)變量X~N(2,9)，則P(X<5)=A.Φ(1)B.Φ(0.5)C.Φ(1.5)D.Φ(2)4.設(shè)隨機(jī)變量X的密度函數(shù)為f(x)=ce^(2x)，x≥0，則常數(shù)c=A.1B.2C.3D.45.設(shè)隨機(jī)變量X和Y相互獨(dú)立，且D(X)=4，D(Y)=9，則D(X2Y)=A.13B.22C.31D.406.設(shè)隨機(jī)變量X服從[0,2]上的均勻分布，則E(X2)=A.1/3B.2/3C.4/3D.8/37.設(shè)隨機(jī)變量X和Y的協(xié)方差為cov(X,Y)=3，且D(X)=4，D(Y)=9，則相關(guān)系數(shù)ρ(X,Y)=A.1/2B.1/3C.1/4D.1/68.設(shè)隨機(jī)變量X服從二項(xiàng)分布B(n,p)，且E(X)=6，D(X)=3.6，則參數(shù)n和p分別為A.n=10,p=0.6B.n=12,p=0.5C.n=15,p=0.4D.n=20,p=0.3第二部分：填空題（共4題，每題5分，共20分）9.設(shè)隨機(jī)變量X的分布函數(shù)為F(x)，則P(a<X≤b)=________________________10.設(shè)隨機(jī)變量X~N(μ,σ2)，若P(X>μ+σ)=0.1587，則P(|Xμ|<σ)=________________________11.設(shè)隨機(jī)變量X和Y獨(dú)立同分布，且E(X)=2，D(X)=3，則E[(X+Y)2]=________________________12.設(shè)隨機(jī)變量X的密度函數(shù)為f(x)=3x2，0≤x≤1，則E(e^X)=________________________第三部分：簡答題（共2題，每題20分，共40分）13.設(shè)隨機(jī)變量X的密度函數(shù)為f(x)=kxe^(x2/2)，x≥0，求：(1)常數(shù)k的值(2)E(X)和D(X)作答空間：______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________14.設(shè)二維隨機(jī)變量(X,Y)的聯(lián)合密度函數(shù)為f(x,y)=6xy，0≤x≤1，0≤y≤1，求：(1)邊緣密度函數(shù)f_X(x)和f_Y(y)(2)判斷X和Y是否獨(dú)立(3)cov(X,Y)作答空間：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________