关于概率统计的题,请给详解 Distribution of minimum of random variables.Let X1 ,X2 ,· · · ,Xn beindependent random variables from an exponential distribution with the density functionf (x) =1/τ* e-x/τ(这里我打不出来,后面是e
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![关于概率统计的题,请给详解 Distribution of minimum of random variables.Let X1 ,X2 ,· · · ,Xn beindependent random variables from an exponential distribution with the density functionf (x) =1/τ* e-x/τ(这里我打不出来,后面是e](/uploads/image/z/8482060-28-0.jpg?t=%E5%85%B3%E4%BA%8E%E6%A6%82%E7%8E%87%E7%BB%9F%E8%AE%A1%E7%9A%84%E9%A2%98%2C%E8%AF%B7%E7%BB%99%E8%AF%A6%E8%A7%A3+Distribution+of+minimum+of+random+variables.Let+X1+%2CX2+%2C%C2%B7+%C2%B7+%C2%B7+%2CXn+beindependent+random+variables+from+an+exponential+distribution+with+the+density+functionf+%28x%29+%3D1%2F%CF%84%2A+e-x%2F%CF%84%28%E8%BF%99%E9%87%8C%E6%88%91%E6%89%93%E4%B8%8D%E5%87%BA%E6%9D%A5%2C%E5%90%8E%E9%9D%A2%E6%98%AFe)
关于概率统计的题,请给详解 Distribution of minimum of random variables.Let X1 ,X2 ,· · · ,Xn beindependent random variables from an exponential distribution with the density functionf (x) =1/τ* e-x/τ(这里我打不出来,后面是e
关于概率统计的题,请给详解
Distribution of minimum of random variables.
Let X1 ,X2 ,· · · ,Xn be
independent random variables from an exponential distribution with the density function
f (x) =1/τ* e-x/τ(这里我打不出来,后面是e的-x/τ次方)
Define the minimum of X1 ,X2 ,· · · ,Xn as
X(1) = min(X1 ,X2 ,· · · ,Xn ).
a.Find the distribution function of X(1) .
b.What is the density function of X(1)
关于概率统计的题,请给详解 Distribution of minimum of random variables.Let X1 ,X2 ,· · · ,Xn beindependent random variables from an exponential distribution with the density functionf (x) =1/τ* e-x/τ(这里我打不出来,后面是e
令Z=X(1) (没什么特殊含义,就是表达起来方便)
用定义F(z)=P{min{X1,X2...Xn}z}
=1-P{X1>z}P{X2>z}...P{Xn>z}=1-[1-P{X