Suppose X 1 , … , X m and Y 1 , … , Y...

Markus Petty

Markus Petty

Answered

2022-07-20

Suppose X 1 , , X m and Y 1 , , Y n are random variables with the property that C o v ( X i , Y j ) < for all i and j. Show that, for any constants a 1 , , a m and b 1 , , b n ,
C o v ( i = 1 m a i X i , j = 1 n b j Y j ) = i = 1 m j = 1 n a i b j C o v ( X i , Y j )

Answer & Explanation

suchonos6r

suchonos6r

Expert

2022-07-21Added 14 answers

x 1 , , x m and y 1 , , y n are random variable with the property that _
c o v ( x i , y j ) <
for all i and j. Show that _
for any constants a 1 , , a m  and  b 1 , b n
c o v ( i = 1 m a i x i , j = 1 n b j Y j ) = i = 1 m j = 1 n a i b j c o v ( x i , Y j )
c o v ( i = 1 m a i x i , j = 1 n b j Y j ) = i = 1 m j = 1 n a i b j ( c o v ( a i x i , b j Y j ) )
= i = 1 m j = 1 n a i b j c o v ( x i , Y j )
Hence, show that for any constant a 1 , , a m  and  b 1 , , b n
c o v ( i = 1 m a i x i , j = 1 m b j Y j ) = i = 1 m j = 1 n a i b j c o v ( X i , Y j )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?