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Variance - 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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