If x_i is defined as x_i = $\pi$_i - E($\pi$_i),and p_i is the probability of occurrence of any x_i,the formula for the square of the standard deviation can be written as: A) $\Sigma$ x_i p_i. B)$\Sigma$ x_i p²_i. C) $\Sigma$x²_i p²_i. D) $\Sigma$x²_i p_i. E)$\Sigma$(x_i p_i)².

Question

Quizplus · Accepted Answer

The formula for the standard deviation is: where μ is the expected value (mean) of x_i, and p_i is the probability of occurrence of any x_i. To simplify the formula, we can square both sides: Expanding the right-hand side and replacing μ with the definition of x_i, we get: Applying linearity of expectation and rearranging, we obtain: which is equivalent to choice D.

If Xi Is Defined as Xi = π\piπ i - E π\piπ

If X_i Is Defined as X_i = $\pi$ _i - E $\pi$