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The joint probability density function of a two-dimensional random variable \((X,Y)\) is \[ f(x,y)= \begin{cases} 2, & 0\\ 0, & \text{otherwise}. \end{cases} \] Which of the following is correct?

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A quick way to detect dependence is to observe the support region. If the support is triangular, circular, or bounded by one variable in terms of another, the variables are generally not independent.

Updated On: Jun 25, 2026

\(X\) and \(Y\) are independent
Marginal density function of \(X\) is \(x,\;0<x<1\)
Marginal density function of \(Y\) is \((1-y),\;0<y<1\)
\(X\) and \(Y\) are not independent

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The Correct Option is D

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The joint probability density function of a two-dimensional random variable \((X,Y)\) is \[ f(x,y)= \begin{cases} 2, & 0\\ 0, & \text{otherwise}. \end{cases} \] Which of the following is correct?

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The Correct Option is D

Solution and Explanation

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