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If cov(x, y) = 15, what restrictions should be put for the standard deviations of x and y?
  • a)
    No restriction.
  • b)
    The product of the standard deviations should be more than 15.
  • c)
    The product of the standard deviations should be less than 15.
  • d)
    The sum of the standard deviations should be less than 15
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If cov(x, y) = 15, what restrictions should be put for the standard de...
Explanation:
The covariance of two variables x and y is defined as the average of the product of the deviations of each variable from its mean.

cov(x, y) = E[(x - E[x])(y - E[y])]

Here, cov(x, y) = 15

To find the restrictions on the standard deviations of x and y, we can use the following formula:

cov(x, y) = E[(x - E[x])(y - E[y])]
= E[xy - xE[y] - yE[x] + E[x]E[y]]
= E[xy] - E[x]E[y] - E[x]E[y] + E[x]E[y]
= E[xy] - E[x]E[y]

Now, let's use the formula for the correlation coefficient:

corr(x, y) = cov(x, y) / (σx * σy)

Here, cov(x, y) = 15, and we want to find the restrictions on σx and σy.

Restrictions on standard deviations of x and y:

- The product of the standard deviations should be more than 15.

If the product of the standard deviations is less than 15, then the correlation coefficient will be greater than 1, which is not possible. Therefore, the product of the standard deviations should be more than 15.

- No restriction on the sum of the standard deviations.

The sum of the standard deviations does not affect the correlation coefficient, so there is no restriction on the sum of the standard deviations.

Therefore, the correct answer is option B.
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Community Answer
If cov(x, y) = 15, what restrictions should be put for the standard de...
The correlation values lies between-1 and 1.
correlation is
covariance (x, y) divided by (sd of X . sd of Y)
Covariance should be less than or equal to denominator to get the value between -1 and 1 . so, this is the reason.
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If cov(x, y) = 15, what restrictions should be put for the standard deviations of x and y?a)No restriction.b)The product of the standard deviations should be more than 15.c)The product of the standard deviations should be less than 15.d)The sum of the standard deviations should be less than 15Correct answer is option 'B'. Can you explain this answer?
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