(X

n

)

(Y

n

)

n ≥ 1 (X

n

)

g

n

(x) =

1

π ·

n

n

2

x

2

+ 1

,

(Y

n

)

P (Y

n

= k) =

1

2

k

+

1

n2

n

, k = 1, 2, . . . , n.

n

X

n

Y

n

(X

n

+ Y

n

)

!

"

#

$

%&

%

"

%

[370, 450]

'

!

"

(

&

#

(X

n

)

n ≥ 1

(X

n

)

P (X

n

=

1

2

n

) = P (X

n

= −

1

2

n

) =

1

2

n

, P (X

n

= 0) = 1 −

1

2

n−1

.

#

!%

'

X

Y

"

X + Y

0

2

X

Y

$

(X

n

)

n ≥ 1

X

n

[− cos

1

n

, cos

1

n

]

(

Y

n

=

X

1

+ X

2

+ . . . + X

n

√

n

%