摩根斯坦笔试题

摩根斯坦利数学题

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.