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Questions › JNU › JNU SIS 2016 › Q49
2 marks, −1Statistics › Joint distributions, covariance and correlation › Joint, marginal and conditional distributionsHardabout 4 min

JNU SIS 2016 Question 49: Joint distributions, covariance and correlation

Let f(x1, x2)=21x12x23f(x_1,\, x_2) = 21x_1^2 x_2^3f(x1​,x2​)=21x12​x23​, for 0<x1<x2<10 < x_1 < x_2 < 10<x1​<x2​<1, and 000 elsewhere, be the joint probability density function of X1X_1X1​ and X2X_2X2​. The conditional mean and variance of X1X_1X1​ given X2=x2, 0<x2<1X_2 = x_2,\ 0 < x_2 < 1X2​=x2​, 0<x2​<1 are

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Let f(x₁, x₂) = 21x₁² x₂³, for 0 < x₁ < x₂ < 1, and 0 elsewhere, be the joint probability density function of X₁ and X₂. The conditional mean and variance of X₁ given X₂ = x₂, 0 < x₂ < 1 are (A) 4x₂ and 6x₂² (B) 0· 3 and 0· 8 (C) 0· 1 and 4 (D) 3/4x₂ and 3/80x₂²

Also written as: Let f(x_1, x_2) = 21x_1^2 x_2^3, for 0 < x_1 < x_2 < 1, and 0 elsewhere, be the joint probability density function of X_1 and X_2. The conditional mean and variance of X_1 given X_2 = x_2, 0 < x_2 < 1 are

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.

TestStop has 14 past-paper questions on this subtopic.

Practise Joint distributions, covariance and correlationMore on Joint, marginal and conditional distributions

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