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If x and y are two uncorrelated variable then which of the following relation is true a)Var(x+y)=Var(x) + Var(y) b)Var(x-y)=Var(x)+Var(y) c)both a) and b) above are true d) only a) above is true?
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If x and y are two uncorrelated variable then which of the following r...

Explanation:

Uncorrelated Variables:
When two variables x and y are uncorrelated, it means that there is no linear relationship between them. In other words, the covariance between x and y is zero.

Relation between Variances:
The variance of the sum or difference of two uncorrelated variables is not simply the sum of their individual variances.

Correct Relation:
The correct relation is:
a) Var(x+y) = Var(x) + Var(y)

This means that the variance of the sum of two uncorrelated variables is equal to the sum of their individual variances.

Explanation:
When two variables are uncorrelated, their covariance is zero. Therefore, when calculating the variance of the sum or difference of these variables, the cross-product terms involving covariance are zero, and we are left with the sum of the individual variances.

Therefore, the correct relation is Var(x+y) = Var(x) + Var(y), and Var(x-y) is not equal to Var(x) + Var(y).
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If x and y are two uncorrelated variable then which of the following relation is true a)Var(x+y)=Var(x) + Var(y) b)Var(x-y)=Var(x)+Var(y) c)both a) and b) above are true d) only a) above is true?
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If x and y are two uncorrelated variable then which of the following relation is true a)Var(x+y)=Var(x) + Var(y) b)Var(x-y)=Var(x)+Var(y) c)both a) and b) above are true d) only a) above is true? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If x and y are two uncorrelated variable then which of the following relation is true a)Var(x+y)=Var(x) + Var(y) b)Var(x-y)=Var(x)+Var(y) c)both a) and b) above are true d) only a) above is true? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are two uncorrelated variable then which of the following relation is true a)Var(x+y)=Var(x) + Var(y) b)Var(x-y)=Var(x)+Var(y) c)both a) and b) above are true d) only a) above is true?.
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