Maharashtra State BoardHSC Arts 12th Board Exam
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The probability mass function for X = number of major defects in a randomly selected appliance of a certain type is - Mathematics and Statistics

The probability mass function for X = number of major defects in a randomly selected
appliance of a certain type is 

X = x 0 1 2 3 4
P(X = x) 0.08 0.15 0.45 0.27 0.05

Find the expected value and variance of X.

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Solution

`E(X)=sumx_i.P(x_i)`

`=0(0.08)+1(0.15)+2(0.45)+3(0.27)+4(0.05)`

`=0+0.15+0.9+0.81+0.2=2.06`

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

`=0(0.08)+1^2(0.15)+2^2(0.45)+3^2(0.27)+4^2(0.05)`

`=0 + 0.15 + 1.8 + 2.43 + 0.8=5.18`

`Var(X)=E(X^2)-[E(X)]^2`

`=5.18-(2.06)^2`

`=5.18-4.2436`

`=0.9364`

Concept: Variance of Binomial Distribution (P.M.F.)
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