摩根斯坦利数学类笔试题

　　参加摩根斯坦利笔试的时候特别注意了一下，试卷的任何部分没有关于试题内容不能泄露的要求。如果确有这样的要求，请删除吧。

　　1. X is a uniform distribution random variable between [0,1], Y=Ln(x). What is the range of values Y can take, and Y's probability distribution function.

　　2. X and Y are independent normal distribution random variables with mean 0 and standard deviation 1. Prove that Z=X+Y is also a normal distribution random variable. What's Z's mean and standard deviation? What's the correlation coefficience between X and Z.

　　3. A binary random variable is a random variable that takes only 2 values 0 and 1. A and B are binary random vriables with

　　Probability(A=1) = 0.3

　　Probability(B=1) = 0.5

　　What is the min and max correlation between A and B.

　　4. Find all solutions to the following ordinary differetial equations.

　　f(x)''+2f(x)'+f(x)=2.




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