If covariance between X & Y is 40 & variance of X is 16, what could be variance of Y?
a.
less than 10
b.
more than 10
c.
more than 100
d.
less than 100
Answers
V(Y) = Variance of Y = 256
Answer:
The correct answer is d. less than 100
Explanation:
From the above question,
They have given :
Covariance = 40
Variance of X = 16
Variance of Y = Covariance + Variance of X
Variance of Y = 40 + 16
Variance of Y = 56
Since 56 is less than 100, the answer is d. less than 100.
The formula for variance is the sum of squared differences of each element from the mean, divided by the number of elements. The covariance is the sum of the products of the differences of each element from the mean of each variable, divided by the number of elements.
Therefore, since the covariance between X and Y is given as 40, and the variance of X is 16, the variance of Y can be calculated by adding the covariance and the variance of X. This will give us the variance of Y, which will be less than 100.
Hence,
The correct answer is d. less than 100
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