Which of the following statements are true? I. Var(X) ≥ 0 for every random variable. II. Var(X + c) = Var(X) for a constant c. III. Var(cX) = c Var(X) for a constant c. IV. The standard deviation is in the same units as X.

Question 65

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Which of the following statements are true?
I. $\text{Var}(X) \ge 0$ for every random variable.
II. $\text{Var}(X + c) = \text{Var}(X)$ for a constant $c$ .
III. $\text{Var}(cX) = c\,\text{Var}(X)$ for a constant $c$ .
IV. The standard deviation is in the same units as $X$ .

All four: I, II, III and IVCorrect answerYour answerI and II onlyCorrect answerYour answerII and IV onlyCorrect answerYour answerI, II and IV onlyCorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

I: a variance is an average of squares. II: shifting every value does not change the spread. IV: the square root undoes the squaring of units.
III is false: $\text{Var}(cX) = c^{2}\,\text{Var}(X)$ .

Concept: Facts about variance
Typical timeTypical: 120 s
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The rule this testsVariance and standard deviation

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