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.