#### 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(X^{2}) - [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

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.