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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.

# Definition

What is the variance of the following probability distribution: $\begin{array} &P(X = -1) = 0.5, &P(X = 0) = 0.2, &P( X = 1) = 0.3 ?\end{array}$

When all values of a dataset are doubled, what happens to the variance?

You throw a coin twice. The prize is $$50$$ dollars if it lands heads, and $$4$$ dollars if it is tails. If $$X$$ is the total prize you will end up receiving, then what is the variance of $$X ?$$

The probability distribution of a random variable $$X$$ is $\begin{array} &P(X = 1) = a, &P(X = 2) = b, &P( X = 3) = 0.4. \end{array}$ If $$a \cdot b=0.05$$ and $$a \geq b,$$ then what is the variance of $$X?$$

The probability distribution of a random variable $$X$$ is $\begin{array} &P(X = 1) = 0.1, &P(X = 2) = 0.2, &P( X = 3) = a.\end{array}$ What is the variance of $$X?$$

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