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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

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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