Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Random Variables & Distribution Functions
Let X and Y be jointly distributed continuous random variables with joint probability density function \(\rm f(x, y)=\left\{\begin{matrix}\frac{x}{y}, & if\ 0
Which of the following statements are true?
1
\(\rm P\left(X<\frac{1}{2}|Y=1\right)=\frac{1}{4}\)
2
E(Y) = \(\frac{1}{4}\)
3
\(\rm P\left(X < \frac{Y}{2}\right)=\frac{1}{4}\)
4
\(\rm E\left(\frac{Y}{X}\right)=\frac{1}{4}\)