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EXERCISE 1

a)

3 2 = 130

3 230

= 322 3

3 = 32

2 3

3+

0

3

3(3)22

(3)33

3(0)22

(0)33

= 272

9272

9 = 1

27

2 9 = 1 92 = 1

= 29

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b)

293 23

2

= 23 2

92 = 2

3

3

2

2327

23

2327

2

3

= 323

2(3)327

223 2(2)3

27 = 3 2 4

3 1627

= 26%

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EXERCISE 2

EXPECTED VALUE

+

=

+

= () +

() ()

+ = .

VARIANCE

+

.

Solving the Integral :

+

= () +

()

() =

+

.

Going back to the original equation:

. . = .

STANDARD DEVIATION

. = .