Question

From a survey of 20 families in a society, the following data wasobtainedNo. of children01234No. of families511202For the random variable X = number of children in a randomlychosen family, Find E(X) and V(X).​

Answer 1

Step-by-step explanation:

Class 9

>>Maths

>>Statistics

>>Graphical Representation of Data

>>A random survey of the number of childre

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A random survey of the number of children of various age group playing in a park was found as follows:

Draw a histogram to represent the data above.

464422

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Solution

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Age

(in years) Frequency Width Length of the

rectangle

1 - 2 5 1

1

5

×1=5

2 - 3 3 1

1

3

×1=3

3 - 5 6 2

2

6

×1=3

5 - 7 12 2

2

12

×1=6

7 - 10 9 3

3

9

×1=3

10 - 15 10 5

5

10

×1=2

15 - 17 4 2

2

4

×1=

Answer 2

Answer:

The answer is E(X)=1.15 & V(X)= 1.2275

Step-by-step explanation:

i) Expected value = E(X) = μ = ∑x.P(x)

=[ 0(5/20) + 1(11/20) + 2(2/20) + 3(0/20) + 4(2/20) ]

=[ (11+4+8)/20 ]

= 23/20

= 1.15

ii) Variance = V(X) = ∑(x-μ$)^{2}$.P(x)

$=[ (0-1.15)^{2} (5/20) + (1-1.15)^{2} (11/20) + (2-1.15)^{2} (2/20) + (3-1.15)^{2} (0/20) + (4-1.15)^{2} (2/20) ]$

= [ (6.6125 + 0.2475 + 1.445 + 0 + 16.245) / 20 ]

= 24.55/20

= 1.2275

iii) Hence,

Expected value E(X)= 1.15

Variance V(X)= 1.2275

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