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Variance

Would you rather get paid $2 for flipping heads, or$6 for rolling a "1"? The expected value is the same (\$1)...but the bets are different! Variance and standard deviation add color to probability.

Standard Deviation

If the standard deviation of the following probability distribution: $\begin{array} &P(X = 0) = 0.2, &P(X = 1) = 0.4, &P( X = 2) = 0.4\end{array}$ is $$A,$$ what is the value of $$A^2?$$

If the standard deviation of the following probability distribution: $\begin{array} &P(X = 0) = 0.1, &P(X = 1) = 0.3, &P( X = 2) = 0.6 \end{array}$ can be expressed as $$\frac{1}{10} \sqrt{A},$$ what is $$A?$$

Imgur

The figure above represents the graphs of the probability density functions of three different probability distributions that have the same mean $$m.$$ Which of the following correctly represents them in order of increasing standard deviation?

Note: Assume that the areas under the curves are all equal to 1.

If the standard deviation of the numbers $$19, 21, 22$$ and $$23$$ is a constant $$m$$, then the standard deviation of the numbers $$21, 23, 24$$ and $$25$$ is $$\text{_________}.$$

What is the standard deviation of the following probability distribution: $\begin{array} &P(X = 4) = \frac{1}{2}, &P( X = 14) = \frac{1}{2} ? \end{array}$

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