设随机变量X的密度函数为。

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设连续型随机变量X的分布函数为<img src='https://img2.soutiyun.com/ask/2020-10-30/972912565646551.png' /> 求系数A, P(0.3＜X ＜0.7),概率密度f(x)。

A.<img src='https://img2.soutiyun.com/ask/2020-10-04/970660847536956.png' /> B.<img src='https://img2.soutiyun.com/ask/2020-10-04/970660856247455.png' /> C.F(a) D.2F(a)-1

设二维随机变量(X，Y)的联合密度函数为 <img src='https://img2.soutiyun.com/ask/2020-08-03/965315924249654.png' /> 求P{X+Y≥1}.

设随机变量X的密度函数如下，试求E(2X+5). <img src='https://img2.soutiyun.com/ask/2020-08-03/965298880343798.png' />

则概率P(X＜0.5，Y＜0.6)为( )． A．0.5 B．0.3 C．<img src='https://img2.soutiyun.com/latex/latex.action' /> D．0.4

设二维随机变量(X，Y)的联合密度函数为 <img src='https://img2.soutiyun.com/ask/2020-08-03/965315602771267.png' /> (1)试求常数k; (2)求P{X＞0.5}和P{Y＜0.5}.

设随机变量X的密度函数为<img src='https://img2.soutiyun.com/ask/2020-12-11/976569159505296.png' />求P(X≤0.5);P(X=0.5);F(x).

设随机变量(X，Y)的联合密度函数为 <img src='https://img2.soutiyun.com/ask/2020-08-03/965319564212848.png' /> 试求E(Y/X).

设随机变量X的密度函数为φ(x)，且φ(－x)＝φ(x)，F(x)为X的分布函数，则对任意实数a，有()． <img src='https://img2.soutiyun.com/ask/uploadfile/2160001-2163000/4fc3fa773ba3ff1b4a790c7f86a536e7.jpg' />

设随机变量X的概率密度为<img src='https://img2.soutiyun.com/ask/2020-11-26/975236522008382.jpg' />，求下列随机变量函数的概率密度： (1)Y₁=2X; (2)Y₂=-X+1; (3)Y₃=X²。

设连续随机变量X的密度函数p(x)是一个偶函数，F(x)为X的分布函数，求证对任意实数a＞0，有 <img src='https://img2.soutiyun.com/ask/2020-08-03/965297607418991.png' />

设随机变量X的密度函数为<img src='https://img2.soutiyun.com/ask/2020-07-29/964865005139989.png' />，已知<img src='https://img2.soutiyun.com/ask/2020-07-29/964864974165217.png' />。(1)求a,b,c的值; (2)求随机变量Y=e^X的数学期望和方差。

设随机变量X的密度函数为<img src='https://img2.soutiyun.com/ask/2020-09-29/970257357637827.png' />，试利用正态分布的密度函数性质求未知参数A的数值。

设二维随机变量(X，Y)的联合密度函数为： <img src='https://img2.soutiyun.com/ask/2020-10-03/970611218878572.png' /> (1)分别求X和Y的边缘密度函数。 (2)求Z=2X-Y的密度函数

设随机变量X与Y独立，并且都服从区间[0,a]均匀分布，求随机变量<img src='https://img2.soutiyun.com/ask/2020-07-29/964864030603248.png' />的密度函数。

设随机变量X的分布密度函数为<img src='https://img2.soutiyun.com/ask/2020-08-05/965469476347499.png' /> 求E(X)及D(X)。