For the probability distribution given by 

 X = xi 

 0 

 1 

 2 

 pi

  

  

  


the standard deviation (σ) is:

  1. None of these

Answer (Detailed Solution Below)

Option 2 :
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Detailed Solution

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Concept:

For a random variable X = xi with probabilities P(X = xi) = pi:

  • Mean/Expected Value: μ = ∑pixi.
  • Variance: Var(X) = σ2 = ∑pi(xi)2 - (∑pixi)2 = ∑pi(xi)2 - μ2.
  • Standard Deviation: σ = .

 

Calculation:

We have x1 = 0, x2 = 1, x3 = 2 and p1, p2, p3.

∑pixi = .

∑pi(xi)2 = .

∴ Var(X) = σ2 = ∑pi(xi)2 - (∑pixi)2 = .

⇒ Standard Deviation = σ = .

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