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-7/15 and7/30 1/5 and-3/5​

Answer 1

Answer:

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Answer 2

Answer:

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

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