Key Takeaways

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Continuous Random Variables

For a continuous random variable \(X\) the only probabilities that are computed are those of \(X\) taking a value in a specified interval.
The probability that \(X\) take a value in a particular interval is the same whether or not the endpoints of the interval are included.
The probability \(P(a < X < b)\), that \(X\) take a value in the interval from \(a\) to \(b\), is the area of the region between the vertical lines through \(a\) and \(b\), above the \(x\)-axis, and below the graph of a function \(f(x)\) called the density function.
A normally distributed random variable is one whose density function is a bell curve.
Every bell curve is symmetric about its mean and lies everywhere above the \(x\)-axis, which it approaches asymptotically (arbitrarily closely without touching).

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