# Engineering probability 2 questions

Anonymous

### Question Description

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

screen_shot_2020_02_17_at_3.45.17_am.png
screen_shot_2020_02_17_at_3.45.32_am.png

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pallveechem123
School: Carnegie Mellon University

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 ] − ExE y 

=

 x y

………..(1)

1 1
1 1
1
1− x2 
 x 2 x3  1 1
dx =  −  =
Ex, 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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