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STATISTICS
There are 4 cards numbered 1,3,5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.
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ANSWER
The 4 cards are numbered as 1,3,5,7
Let S be the sample space and we have 4×3=12 elements in sample space
Here X is sum of numbers on two drawn cards , X can be 4,6,8,10,12
P(X=4)=
12
2
=
6
1
P(X=6)=
12
2
=
6
1
P(X=8)=
12
4
=
3
1
P(X=10)=
12
2
=
6
1
P(X=12)=
12
2
=
6
1
∑P
i
X
i
=4×
6
1
+6×
6
1
+8×
3
1
+10×
6
1
+12×
6
1
=
6
4+6+16+10+12
=
6
48
=8
Therefore the mean is 8
∑P
i
X
i
2
=4
2
×
6
1
+6
2
×
6
1
+8
2
×
3
1
+10
2
×
6
1
+12
2
×
6
1
=
6
16+36+128+100+144
=
6
424
=
3
212
The variance is
3
212
−64=
3
20
Answered By
toppr
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