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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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