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Questions › IIT JAM › IIT JAM 2023 › Q40
2 marksStatistics › Joint distributions, covariance and correlation › Joint, marginal and conditional distributionsHardabout 3 min

IIT JAM 2023 Question 40: Joint distributions, covariance and correlation

Let f(x,y)=1f(x,y)=1f(x,y)=1 for 0<x<10<x<10<x<1, x<y<x+1x<y<x+1x<y<x+1, and 000 otherwise. Which are CORRECT for the marginals and moments?

Select all that apply.

Answer and worked solution

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Plain-text version

Let f(x,y)=1 for 0<x<1, x<y<x+1, and 0 otherwise. Which are CORRECT for the marginals and moments? (A) f_X(x)=2x on (0,1) and f_Y(y)=2-y on (0,2) (B) f_X(x)=1 on (0,1) and f_Y(y)=y on (0,1), 2-y on (1,2) (C) E(X)=1/2, Var(X)=1/12 (D) E(Y)=1, Var(Y)=1/6

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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