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Class 12-commerce RD SHARMA Solutions Maths Chapter 32: Mean and variance of a random variable

Mean and variance of a random variable Exercise Ex. 32.1

Solution 1

Solution 2

Solution 3

Solution 4


Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12


Solution 13

 

Solution 14


Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

 

Solution 29

 

Mean and variance of a random variable Exercise Ex. 32.2

Solution 1(i)

 

Solution 1(ii)


Solution 1(iii)



Solution 1(iv)


Solution 1(v)


Solution 1(vi)


Solution 1(vii)


Solution 1(viii)


Solution 1(ix)

 

Solution 2

 

Solution 3


Solution 4



Solution 5



Solution 6


Solution 7

Solution 8



Solution 9



Solution 10



Solution 11



Solution 12

Solution 13





Solution 14



Solution 15

Solution 16

Solution 17

begin mathsize 12px style table attributes columnalign left end attributes row cell Let text    end text apostrophe straight X apostrophe text    end text be text    end text the text    end text random text    end text variable text    end text which text    end text can text    end text assume end cell row cell values text    end text from text    end text 0 text    end text to text    end text 3. end cell row cell straight P left parenthesis straight X equals 0 right parenthesis equals fraction numerator blank to the power of 26 straight C subscript 3 over denominator blank to the power of 52 straight C subscript 3 end fraction equals 2600 over 22100 equals 2 over 17 end cell row cell straight P left parenthesis straight X equals 1 right parenthesis equals fraction numerator blank to the power of 26 straight C subscript 1 cross times to the power of 26 straight C subscript 2 over denominator blank to the power of 52 straight C subscript 3 end fraction equals 8450 over 22100 equals 13 over 34 end cell row cell straight P left parenthesis straight X equals 2 right parenthesis equals fraction numerator blank to the power of 26 straight C subscript 2 cross times to the power of 26 straight C subscript 1 over denominator blank to the power of 52 straight C subscript 3 end fraction equals 8450 over 22100 equals 13 over 34 end cell row cell straight P left parenthesis straight X equals 3 right parenthesis equals fraction numerator blank to the power of 26 straight C subscript 3 over denominator blank to the power of 52 straight C subscript 3 end fraction equals 2600 over 22100 equals 2 over 17 end cell row cell Probability text    end text distribution text    end text of text    end text straight X colon end cell row cell table row cell straight X equals straight x subscript straight i end cell 0 1 2 3 row cell straight p left parenthesis straight X equals straight x subscript straight i right parenthesis end cell cell 2 over 17 end cell cell 13 over 34 end cell cell 13 over 34 end cell cell 2 over 17 end cell end table end cell row blank row cell Mean equals sum from straight i equals 0 to 3 of left parenthesis straight x subscript straight i cross times straight p subscript straight i right parenthesis end cell row cell equals straight x subscript 0 straight p subscript 0 plus straight x subscript 1 straight p subscript 1 plus straight x subscript 2 straight p subscript 2 plus straight x subscript 3 straight p subscript 3 end cell row cell equals 0 cross times 2 over 17 plus 1 cross times 13 over 34 plus 2 cross times 13 over 34 plus 3 cross times 2 over 17 end cell row cell equals fraction numerator 13 plus 26 plus 12 over denominator 34 end fraction end cell row cell equals 51 over 34 end cell row cell equals 3 over 2 end cell row cell equals 1.5 end cell end table end style

Solution 18

 

Solution 19

 

Mean and variance of a random variable Exercise MCQ

Solution 1

Correct option: (d)

 

Solution 2

Correct option: (b)

 

Solution 3

Correct option: (d)

 

Solution 4

Correct option: (a)

 

 

Solution 5

Correct option: (d)

 

Solution 6

Correct option: (c)

NOTE: Question is modified. 

Solution 7

Correct option: (d)

 

 

Solution 8

Correct option: (d)

 

Solution 9

Correct option: (c)

Variance of discrete random variable is always E(X2) - (E(X))2

 

Mean and variance of a random variable Exercise Ex. 32VSAQ

Solution 1

Solution 2

Solution 3



Solution 4

Solution 5

Solution 6

rightwards double arrow P left parenthesis x less or equal than 2 right parenthesis equals 0.3

Solution 7

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