2) 52 51
221
C
2 (52
2) P(X = 1) = P (one king and one non-king) 
4
148
1
52
2
C
CC
=
   = 4 48 2
32
52 51
221
×
× =
×
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not to be republished
PROBABILITY      569
and
P(X = 2) = P (two kings) =
4
2
52
2
C
4 3
1
52 51
221
C
×
=
=
×
Thus,  the probability distribution of  X is
X
0
1
2
P(X)
188
221
32
221
1
221
Now                           Mean of
X = E(X) = 
1
(
)
n
i
i
i
x p x
  
=
188
32
1
34
0
1
2
221
221
221
221
×
+ ×
+ ×
=
Also
E(X2) =
2
1
(
)
n
i
i
i
x p x
=∑
=
2
2
2
188
32
1
36
0
1
2
221
221
221
221
×
+
×
+
×
=
Now
Var(X) = E(X2) – [E(X)]2
=
2
2
36
34
6800
221–
221
(221)
⎛
⎞ =
⎜
⎟
⎝
⎠
Therefore
σx =
6800
Var(X)
0