1. Let the number of trees that grow in a region of area A have a Possion distribution with expectation λA .Find the expected value of the distance from a certain tree to its nearest neighbor? 2. Let X and Y be two random variable with joint pdf f(x,y).If E[Y|X=x] is a linear function of x, that is , if E[Y|X=x]=a+bx,for some a,b. then E[Y|X=x]= Uy + p*(SigmaY/SigmaX)*(x-Ux). Uy,Ux分別表y,x的平均 SigmaY SigmaX 表 y,x的標準差 p表相關係數 sorry...因為這些符號不會打.... 我只知道第二題符合二為高斯 但是為什麼卻不清楚 3. Let X and be independent random variables each geometrically distributed with parameter p ,i.e P[X=x]=p(1-p)^x ,x=0,1,2... Please find the distribution of min(X,Y) 4. Let X denote the life length of a certain type of electronic componect. These components frequently fail immediately upon insertion into a system. It has been observed that the probability of immediate failure is 1/3. If a component does not fail immediately, its life-length distribution has exponential f(x)=e^(-x) , x>0 Find the distribution function for X and evaluate P(X>10) 麻煩各位大大解答一下 --

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