Coefficient of correlation between the variables x and y is 0.8 and their covariance is 20, the variance of x is 16. standard deviation of y is
Answers
Given:
Coefficient of correlation between the variables x and y is 0.8 and their covariance is 20, the variance of x is 16.
To find:
Find the standard deviation of y
Solution:
We use the below formula to find the standard deviation of y.
r = cov(x, y) / [ √(V(x)) × √(V(y)) ].
where, r = coefficient of correlation
From given, we have,
0.8 = 20 / [ √16 × √(V(y)) ]
⇒ √(V(y)) = 20 / (4 × 0.8) = 6.25
⇒ σ = √V(y) = 6.25.
Therefore, the standard deviation of y is 6.25.
Given : Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20
the variance of X is 16,
To Find : the standard deviation of Y
Solution :
Correlation coefficient = cov (x,y)/ (std deviation (x) ×std deviation (y))
Correlation coefficient = 0.8
cov (x,y) = 20
variance of X is 16.
variance = (standard deviation ) ²
=> std deviation (X) = √variance of X = √16 =4
Substituting values
=> 0.8 = 20 / ( 4 * std deviation (y))
=> 0.8 = 5 / std deviation (y))
=> std deviation (y) = 5 / ( 0.8)
=> std deviation (y) = 6.25
standard deviation of Y is = 6.25
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