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# Understanding Data

Whether you're trying to analyze a political poll, the results of a scientific study, or just your sleeping habits, data is the best tool for understanding the world around you. Dive in and see how!

The probability distribution of a random variable \(X\) is

\[\begin{array} &P(X = 1) = 0.1 &P(X = 2) = 0.2 &P( X = 3) = 0.3 &P( X = 4) = 0.4. \end{array}\]

If \( Y = 9X+14,\) what is the variance of \(Y?\)

If \( V(X) = 4 \), what is \( V(2X + 7 )? \)

If \( V(X) = 3 \) and \(E(X^2) = 10,\) what is \( (E(X))^2 ? \)

If \( V(X) = 5 \), what is \( V(2X + 4 )? \)

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