Maharashtra State BoardHSC Arts 12th Board Exam
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Find the Variance and Standard Deviation of the Random Variable X Whose Probability Distribution is Given Below : - Mathematics and Statistics

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Sum

Find the variance and standard deviation of the random variable X whose probability distribution is given below :

x 0 1 2 3
P(X = x) `1/8` `3/8` `3/8` `1/8`
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Solution

`x_i` `p_i` `p_ix_i` `p_ix_i^2`
0 1/8 0 0
1 3/8 3/8 3/8
2 3/8 6/8 12/8
3 1/8 3/8 9/8
  Total 12/8 24/8 = 3

`E(X) = mu = sump_ix_i = 12/8 = 3/2`

`Var(X) = sum_(i=1)^n p_ix_i^2 - mu^2`

`= 3 - (3/2)^2`

`=3 - 9/4`

`= 3/4`

`∴ Var(X) = sigma^2 = 3/4`

Standard deivation of (X) = `sigma_x = sqrt(3/4) =sqrt3/2`

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