HSC Arts 12th Board ExamMaharashtra State Board
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Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below: 

X=x 1 2 3

P(X=x)

1/5 2/5 2/5

Solution

`E(X)=sumx_iP(x_i)`

=1(1/5)+2(2/5)+3(2/5)

=(1+4+6)/5=11/5

=2.2

`E(X^2)=sumx_i^2P(x_i)`

=1^2(1/5)+2^2(2/5)+3^2(2/5)

=(1+8+18)/5=27/5

=5.4

Var (X) = E(X2) - [E(X)]2

 = 5.4 - (2.2)2
= 5.4 - 4.84
= 0.56

`S.D. = sqrt(Var (X)) = sqrt0.56 = 0.7483`

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APPEARS IN

 2014-2015 (October) (with solutions)
Question 6.2.3 | 4.00 marks
Solution Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below Concept: Probability Distribution - Expected Value, Variance and Standard Deviation of a Discrete Random Variable.
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