- Thread starter
- #1

#### Barioth

##### Member

- Jan 17, 2013

- 52

Hi, I have these 2 problem, that I'm not so sure how to handle.

1-Let \(\displaystyle X_1,X_2,...,X_n\) independant Random variable that all follow a continuous uniform distribution in (0,1)

a) Find \(\displaystyle E[Max(X_1,X_2,...,X_n)]\)

b) Find \(\displaystyle E[Min(X_1,X_2,...,X_n)]\)

where E is for the mathematical expectation. I'm not so sure how to tackle such a question.

2-Let\(\displaystyle X_1, X_2, X_3 and X_4\) are Random variable with no correlation two by two.

Each with mathematical expectation = 0 and variance =1. Evaluate the Correlation for

a-\(\displaystyle X_1+X_2 and X_2+X_3\)

b-\(\displaystyle X_1+X_2 and X_3+X_4\)

I know that \(\displaystyle Corr(X_1+X_2,X_2+X_3)=\frac{Cov(X_1+X_2,X_2+X_3)}{ \sqrt {Var(X_1+X_2)*Var(X_2+X_3)}}\)

All I can think of is using the CTL, but since I don't know if they're independant I can't use it? Also we've seen the CTL after been giving this problem.

Thanks for passing by!

1-Let \(\displaystyle X_1,X_2,...,X_n\) independant Random variable that all follow a continuous uniform distribution in (0,1)

a) Find \(\displaystyle E[Max(X_1,X_2,...,X_n)]\)

b) Find \(\displaystyle E[Min(X_1,X_2,...,X_n)]\)

where E is for the mathematical expectation. I'm not so sure how to tackle such a question.

2-Let\(\displaystyle X_1, X_2, X_3 and X_4\) are Random variable with no correlation two by two.

Each with mathematical expectation = 0 and variance =1. Evaluate the Correlation for

a-\(\displaystyle X_1+X_2 and X_2+X_3\)

b-\(\displaystyle X_1+X_2 and X_3+X_4\)

I know that \(\displaystyle Corr(X_1+X_2,X_2+X_3)=\frac{Cov(X_1+X_2,X_2+X_3)}{ \sqrt {Var(X_1+X_2)*Var(X_2+X_3)}}\)

All I can think of is using the CTL, but since I don't know if they're independant I can't use it? Also we've seen the CTL after been giving this problem.

Thanks for passing by!

Last edited: