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Questions › GATE › GATE 2024 › Q48
2 marks, −0.667Statistics › Joint distributions, covariance and correlation › Joint, marginal and conditional distributionsHardabout 3 min

GATE 2024 Question 48: Joint distributions, covariance and correlation

If XXX and YYY are two random variables with the joint probability density function

f(x,y)={23(x+2y)for 0<x,y<10otherwisef(x,y) = \begin{cases} \dfrac23(x+2y) & \text{for } 0<x,y<1 \\ 0 & \text{otherwise} \end{cases}f(x,y)=⎩⎨⎧​32​(x+2y)0​for 0<x,y<1otherwise​

then E[X∣Y=12]E\left[X \mid Y=\dfrac12\right]E[X∣Y=21​] will be

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If X and Y are two random variables with the joint probability density function f(x,y) = { 2/3(x+2y) for 0<x,y<1; 0 otherwise } then E[X | Y=1/2] will be (A) 5/9 (B) 4/9 (C) 1/3 (D) 2/3

Joint distributions, covariance and correlation has come up 61 times in 7 exams since 2005.

What this question tests

This question is on Joint, marginal and conditional distributions, part of Joint distributions, covariance and correlation in Statistics.

How two random variables behave together and separately.

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