Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Independent Random Variables
Let X1 and X2 be independent and identically distributed standard normal variables. Then which of the following statements are correct?
1
Expected value of max(X1, X2) is \(\frac{1}{\sqrt\pi}\)
2
Conditional expectation of X1 given X1 + X2 is 0.5 (X1 + X2).
3
X1 - X2 and X1 + X2 are independent.
4
\(X_1^2+X_2^2\) and \( \frac{X_1}{X_2}\) and are independent.