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If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y?
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If cov(X,Y)=15, what is restrictions should we put standard deviation ...
Restrictions on Standard Deviation of X and Y given Covariance
When we have the covariance between two variables X and Y, we can determine some restrictions on their standard deviation. The covariance between X and Y is given by:
Cov(X,Y) = E[(X - E[X])(Y - E[Y])]
where E[X] and E[Y] are the expected values of X and Y, respectively.
Positive Covariance
If the covariance between X and Y is positive, i.e., Cov(X,Y) > 0, then:
- Both X and Y tend to increase or decrease together.
- The standard deviation of X and Y must be positive.
- The standard deviation of X and Y cannot be zero.
- The standard deviation of X and Y can be anything greater than zero.
Negative Covariance
If the covariance between X and Y is negative, i.e., Cov(X,Y) < 0,="" />
- X tends to increase when Y decreases and vice versa.
- The standard deviation of X and Y must be positive.
- The standard deviation of X and Y cannot be zero.
- The standard deviation of X and Y can be anything greater than zero.
Zero Covariance
If the covariance between X and Y is zero, i.e., Cov(X,Y) = 0, then:
- X and Y are independent of each other.
- The standard deviation of X and Y can be anything greater than or equal to zero.
- If the standard deviation of X or Y is zero, then the variable is constant and not informative.
Conclusion
In conclusion, the covariance between X and Y provides information about their linear relationship. The standard deviation of X and Y must be positive and cannot be zero. If the covariance is zero, then the variables are independent, and their standard deviations can be anything greater than or equal to zero.
Community Answer
If cov(X,Y)=15, what is restrictions should we put standard deviation ...
The product of standard deviations must be greater than covariance i.e. 15
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If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y?
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If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y?.
If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cov(X,Y)=15, what is restrictions should we put standard deviation of X and y?.
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