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If X is a random variable with Mean μ, then the variance of X, denoted by Var (X) is given by:
  • a)
    Var (X) = E[X] - μ2
  • b)
    Var (X) = E[X2] - μ
  • c)
    Var (X) = E[(X - μ)]2
  • d)
    Var (X) = E[(X - μ)]
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If X is a random variable with Mean μ, then the variance of X, deno...
Explanation:
If X is a random variable with mean μ, then the variance of X, denoted by Var (X) is given by:
Var (X) = E[(X - μ)]2, where μ = E(X)
For a discrete random variable X, the variance of X is obtained as follows:
where the sum is taken all over the values of x for which pX(x) > 0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function pX(x) of X.
Important Points
  • The standard deviation of X is defined as the square root of the variance.
  • The variance cannot be negative, because it is an average of squared quantities.
  • Var (X) is often denoted as σ2.
Hence, If X is a random variable with mean μ, then the variance of X, denoted by Var (X) is given by Var (X) = E[(X - μ)]2
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If X is a random variable with Mean μ, then the variance of X, denoted by Var (X) is given by:a)Var (X) = E[X] -μ2b)Var (X) = E[X2] -μc)Var (X) = E[(X - μ)]2d)Var (X) = E[(X - μ)]Correct answer is option 'C'. Can you explain this answer?
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