If

f

(

x

1

,x

2

)

=

e

x

1

x

2

,

0

<

x

1

<

,

0

<

x

2

<

, zero elsewhere, is the joint pdf of the

random variables X1 and X2, show that X

1

and X

2

are independent and that

M

(

t

1

,t

2

)

=(

1

t

1

)

1

(

1

t

2

)

1

,t

1

<

1,

t

2

<

1

. Also show that

E

(

e

t

(

X

1

+

X

2

)

)

=(

1

t

)

2

,t

<

1