摩根斯坦利数学题

自己的背景实际上不适合这个职位，估计是当分母了。把记得部分笔试题发出来，当攒R
P了。希望能收到dream offer。
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，请斑竹删除吧。

1. X is a uniform distribution random variable between [0,1], Y=Ln(x). What i
s 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 a
nd standard deviation 1. Prove that Z=X+Y is also a normal distribution rando
m variable. What's Z's mean and standard deviation? What's the correlation co
efficience between X and Z.

3. A binary random variable is a random variable that takes only 2 values 0 a
nd 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.