*label*Mathematics

### Question Description

Please find below the 2 attached questions. I need the solution typed with all the work shown.

### Unformatted Attachment Preview

## Tutor Answer

both done

Question 4.52

The correlation coefficient of X and Y, denoted Corr(X,Y) or xy is defined as:

xy =

Cov ( x, y )

x y

E[ x, y ] − ExE y

=

x y

………..(1)

1 1

1 1

1

1− x2

x 2 x3 1 1

dx = − =

Ex, y = xyf ( x, y)dydx = 2 xydydx = 2 x

3 0 6

2

2

0 x

0 x

0

1

1

x

x

f X ( x) = f XY ( x, y)dy = 2dy = 2(1 − x)

y

y

0

0

f y ( x) = f XY ( x, y)dx = 2dy = 2 y

y2...

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