Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Independent Random Variables
Let X1,...Xn be independent and identically distributed U(0, θ), θ > 0 random variables Define X(n) = max{X1....Xn} and X(1) = min{X1..., Xn}. Which of the following statements are true?
1
\(\rm Cov\left(\frac{X_{(n)}}{X_{(1)}}, X_{(n)}\right)=0\)
2
\(\rm E\left(\frac{X_{(1)}}{X_{(n)}}\right)=\frac{E(X_{(1)})}{E(X_{(n)})}\)
3
\(\rm Cov\left(\frac{X_{(1)}}{X_{(n)}}, X_{(n)}\right)=0\)
4
Cov(lnX(1)) - ln(X(1) + X(n)), X(n)) < 0