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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 - Mathematics and Statistics

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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:

 X=x 1 2 3 P(X=x) 1/5 2/5 2/5
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#### 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

Concept: Probability Distribution - Expected Value, Variance and Standard Deviation of a Discrete Random Variable
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