Question

What is a random number? and what are the criteria for a random number? For a research need that requires random numbers, a random number generator is needed, how does this random number generator work?

Answer 1

Random number can be thought of as a realized value of a random variable. Random process is something whose outcome is not known before the happening of the event. When we map the events with a number, then we say the Variable is random variable and realized values are Random numbers.

Now, Random variables are characterized by an underlying distribution. This distribution tells us what is the probability of obtaining a particular number. Like tossing a fair coin gives us 0.5 probability of heads and 0.5 probability of tails. If we assign heads to 1 and tails to 0. We get a random variable X(say) which can take value 1 or 0 with probability 0.5. When we actually toss a coon, X can take value 1 or 0. This 1 or 0 is a Random number.

To generate a random number, we carry out many transformation from an actual random process and get a Random variable with desired distribution. Then we perform the actual process, and get our random numbers much like the example in coin toss. Different distribution of numbers need different processes.