Question

Given the following data with n=5, compute the covariance sxy. Give an exact answer. x 2 3 5 9 11

y -21 -15 -18 -10 -5

Note that ∑i=15xi=30, ∑i=15x2i=240, ,∑i=15yi=−69, ∑i=15y2i=1115

Answer 1

the necessary calculation table:-

xi	yi	$x_{i}y_{i}$
2	-21	-42
3	-15	-45
5	-18	-90
9	-10	-90
11	-5	-55
		sum= -322

the covariance (sample) is :-

677-6( “ = fis

30 * -69. -322 -

$=\mathbf{23}$

i am calculating the population covariance also,for your better understanding.

$\sigma_{xy}=\frac{1}{n}[\sum x_{i}y_{i}-\frac{\sum x_{i}\sum y_{i}}{n}]$

  

30 * -69,

   (this is the population covariance)

= 18.4

*** if you have any doubt regarding the problem please write it in the comment box.if you are satisfied please give me a LIKE if possible...