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Question: Covariance \((x,y)\) between x and y, if \(\sum_{}^{}{x = 15}\), \(\sum_{}^{}{y = 40}\), \(\sum_{}^{...

Covariance (x,y)(x,y) between x and y, if ∑x=15\sum_{}^{}{x = 15}, ∑y=40\sum_{}^{}{y = 40}, ∑x.y=110,n=5\sum_{}^{}{x.y = 110,}n = 5 is

A

22

B

2

C

– 2

D

None of these

Answer

– 2

Explanation

Solution

Given, ∑x=15,∑y=40\sum_{}^{}{x = 15,\sum_{}^{}{y = 40}}

∑x.y=110,n=15\sum_{}^{}{x.y = 110,}n = 15

We know that, Cov(x,y)=1n∑i=1nxi.yi−(1n∑i=1nxi)(1n∑i=1nyi)Cov(x,y) = \frac{1}{n}\sum_{i = 1}^{n}{x_{i}.y_{i} - \left( \frac{1}{n}\sum_{i = 1}^{n}x_{i} \right)\left( \frac{1}{n}\sum_{i = 1}^{n}y_{i} \right)}

=1n∑x.y−(1n∑x)(1n∑y)= \frac{1}{n}\sum_{}^{}{x.y} - \left( \frac{1}{n}\sum_{}^{}x \right)\left( \frac{1}{n}\sum_{}^{}y \right)

=15(110)−(155)(405)=22−3×8=−2= \frac{1}{5}(110) - \left( \frac{15}{5} \right)\left( \frac{40}{5} \right) = 22 - 3 \times 8 = - 2.