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If x and y are two correlated variable then which of the following is true a)Var(x+y)= Var(x)+Var(y)+2Cov(x,y) b)Var(x+y)=Var(x)+Var(y) c)Var(x-y)=Var(x)-Var(y) d) None of the above is true?
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If x and y are two correlated variable then which of the following is ...
Answer:
Introduction:
When two variables are correlated, their joint variability changes. In statistics, this relationship can be quantified using the concepts of covariance and variance.
Explanation:
- Option a: Var(x+y) = Var(x) + Var(y) + 2Cov(x,y)
This statement is true. The variance of the sum of two variables is equal to the sum of their individual variances plus twice the covariance between them.
- Option b: Var(x+y) = Var(x) + Var(y)
This statement is not true. The variance of the sum of two variables is not simply the sum of their individual variances, as it also depends on the covariance between them.
- Option c: Var(x-y) = Var(x) - Var(y)
This statement is also not true. The variance of the difference between two variables is not equal to the difference of their individual variances. It also depends on the covariance between them.
- Conclusion:
In conclusion, when two variables are correlated, their joint variability is influenced by both their individual variances and their covariance. Option a is the correct statement as it correctly accounts for the variances and covariance of the variables x and y.
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If x and y are two correlated variable then which of the following is true a)Var(x+y)= Var(x)+Var(y)+2Cov(x,y) b)Var(x+y)=Var(x)+Var(y) c)Var(x-y)=Var(x)-Var(y) d) None of the above is true?
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If x and y are two correlated variable then which of the following is true a)Var(x+y)= Var(x)+Var(y)+2Cov(x,y) b)Var(x+y)=Var(x)+Var(y) c)Var(x-y)=Var(x)-Var(y) d) None of the 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 correlated variable then which of the following is true a)Var(x+y)= Var(x)+Var(y)+2Cov(x,y) b)Var(x+y)=Var(x)+Var(y) c)Var(x-y)=Var(x)-Var(y) d) None of the 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 correlated variable then which of the following is true a)Var(x+y)= Var(x)+Var(y)+2Cov(x,y) b)Var(x+y)=Var(x)+Var(y) c)Var(x-y)=Var(x)-Var(y) d) None of the above is true?.
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