Random Numbers

Usually when people say they chose something "randomly", they mean uniformly random. That is, every choice has an equal chance of being chosen. There are many other useful ways to think of randomness, when some choices are more likely than others. The most familiar formal distribution (after the uniform distribution) is the Gaussian or normal distribution. In this case, numbers are most likely to be concentrated around a mean. The chances of choosing a number either greater or less than the mean decreases the farther that number is from the mean. This is a continuous distribution, meaning that the numbers chosen can be any real number. There is no maximum or minimum possible number to be chosen from the Gaussian distribution.

Several Gaussian distributions (my notes in purple)

Unlike the Gaussian, the uniform distribution could be either continuous or discrete. If it is discrete, the random numbers chosen from it must be integers. Also, the uniform distribution has both a minimum value and a maximum value, that are defined for each uniform distribution. That is, no number smaller than the minimum can be chosen and no number larger than the maximum can be chosen. However, the minimum and maximum values can be different for different uniform distributions.

Discrete uniform distribution (from Wikipedia, my notes in purple)

Continuous uniform distribution (from Wikipedia, my notes in purple)