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Question: For a bivariate distribution (x, y) if \(\sum_{}^{}{x = 50}\), \(\sum_{}^{}{y = 60}\), \(\sum_{}^{}{...

For a bivariate distribution (x, y) if ∑x=50\sum_{}^{}{x = 50}, ∑y=60\sum_{}^{}{y = 60}, ∑xy=350,x‾=5,y‾=6\sum_{}^{}{xy} = 350,\overline{x} = 5,\overline{y} = 6 variance of x is 4, variance of y is 9, then r(x,y)r(x,y) is

A

5/6

B

5/36

C

11/3

D

11/18

Answer

5/6

Explanation

Solution

x‾=∑xn\overline{x} = \frac{\sum_{}^{}x}{n}⇒ 5=50n5 = \frac{50}{n}⇒n=10n = 10.

∴Cov(x,y)=∑xyn−x‾.y‾=35010−(5)(6)Cov(x,y) = \frac{\sum_{}^{}xy}{n} - \overline{x}.\overline{y} = \frac{350}{10} - (5)(6) = 5.

∴ r(x,y)=Cov(x,y)σx.σy=54.9r(x,y) = \frac{Cov(x,y)}{\sigma_{x}.\sigma_{y}} = \frac{5}{\sqrt{4}.\sqrt{9}} =56\frac{5}{6}.