# Find the Variance and Standard Deviation of the Random Variable X Whose Probability Distribution is Given Below : - Mathematics and Statistics

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

#### 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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