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In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is
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- 0.18
- 0.36
- 0.54
- 0.6
Correct Option: D
Given
mean (μ) = exp(x) = 1 × 0.3 + 2 × 0.6 + 3 × 0.1
= 0.3 + 1.2 + 0.3 = 1.8
E(x2) = ∑ x2P(x)
= 1 × 0.3 + 4 × 0.6 + 9 × 0.1
= 0.3 + 2.4 + 0.9 = 3.6
Variance v (x) = E (x2) – μ2 = 3.6 – (1.8)2
S.D(σ) = + √υ(x)
= + √3.6 - (1.8)2
= √0.36 = 0.6
