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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!

# Variance - Properties

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 $$Y?$$

A random variable $$X$$ has $$E(X)=3$$ and $$V(X)=9.$$ If $\begin{array} &Y=aX+b, &E(Y)= 6, &V(Y) = 9,\end{array}$ what are $$a(>0)$$ and $$b?$$

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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