Random Number Generation

• Math.random() is a method in the Math class whose return value a number, n, of type double, where 0 <= n < 1.
• If we want to produce a set of random numbers in the interval [low, high), we can translate and scale the returned value of Math.random() as follows:

int scaled, translatedAndScaled; // low <= translatedAndScaled < high

scaled = (int) Math.random() * (high - low);

translatedAndScaled = low + scaled;

Why?

Since the lowest value returned by Math.random() is 0, and the highest value is just under 1, we have:

0 = 0 * (high - low) <= Math.random() * (high - low) < 1 * (high - low) = high - low

or, more simply

0 <= Math.random() * (high - low) < high - low

By adding low to this, we obtain:

low <= low + Math.random() * (high - low) < high - low + low = high

Thus, low <= translatedAndScaled < high.

• Let's use this fact to write an applet that produces numbers on the face of a die....lot's of these numbers.