Question

15. If x2 = 2291, 2 y = 3056, S(x + y)2 = 10623, n = 10,x= 14.7.5 = 17
then cov(x, y) is
A139
B 13.9
o 139
D. -13.9​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{If \: \sum {x}^{2} = 2291 , \sum {y}^{2} = 3056 , \sum {(x + y)}^{2} = 10623,n = 10, \bar{x} = 14.7, \bar{y} = 17,n = 10 }$

then cov(x, y) is

A. 0.39

B. 13.9

C. 139

D. - 13.9

EVALUATION

Here it is given that

$\sf{\sum {x}^{2} = 2291 , \sum {y}^{2} = 3056 , \sum {(x + y)}^{2} = 10623,n = 10, \bar{x} = 14.7, \bar{y} = 17,n = 10 }$

Now

$\sf{ \sum {(x + y)}^{2} = 10623}$

$\sf{ \implies \: \sum ({x}^{2} + 2xy + {y}^{2} ) = 10623}$

$\sf{ \implies \: \sum {x}^{2} + \sum \: 2xy + \sum \: {y}^{2} = 10623}$

$\sf{ \implies \:2291 + 2\sum \: xy + 3056 = 10623}$

$\sf{ \implies \sum \: xy = 2638}$

Now

$\displaystyle\sf{Cov(x, y) = \frac{1}{n} \sum \: xy - \bigg( \frac{ \sum \: x}{n} \bigg) \bigg( \frac{ \sum \: y}{n} \bigg)}$

$\displaystyle\sf{ \implies \: Cov(x, y) = \frac{1}{n} \sum \: xy - \bar{x} \: .\: \bar{y}}$

$\displaystyle\sf{ \implies \: Cov(x, y) = \frac{1}{10} \sum \: xy - \bar{x} \: .\: \bar{y}}$

$\displaystyle\sf{ \implies \: Cov(x, y) = \frac{2638}{10} - (14.7 \times 17)}$

$\displaystyle\sf{ \implies \: Cov(x, y) =263.8 - 249.9 }$

$\displaystyle\sf{ \implies \: Cov(x, y) = 13.9 }$

FINAL ANSWER

Hence the correct option is B. 13.9

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Answer 2

Answer:13.9

Step-by-step explanation: