How do you generate such a random number if you are given a coin with unknown bias?

How do you generate such a random number if you are given a coin with unknown bias?

One way to generate such a random variable is to:

1. Toss the coin twice.
2. If the result is HT, assign X=0. If the result is TH, assign X=1.
3. If the result is either HH or TT, then discard the two coin tosses and go to step 1.

How do you create a fair probability using a biased coin?

Riddler Classic. Mathematician John von Neumann is credited with figuring out how to take a biased coin (whose probability of coming up heads is p, not necessarily equal to 0.5) and “simulate” a fair coin. Simply flip the coin twice. If it comes up heads both times or tails both times, then flip it twice again.

How can you use a biased coin to make an unbiased decision?

How can you use a biased coin to make an unbiased decision? That is to say the coin does not give heads or tales with equal probability….Von Neumann wrote it like this:

1. Toss the coin twice.
2. If the results match, start over, forgetting both results.
3. If the results differ, use the first result, forgetting the second.

What is biased coin randomization?

So instead of giving the patient a 50:50 chance of being in treatment or control, randomization uses the “biased coin”: the computer selects a random number between 0 and 1 and if this is less than, say, 0.6 (rather than 0.5 as usual), the patient is assigned to control.

Can you get a biased coin?

Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than sim- ply ipped in the air.

How to make a biased coin from a coin?

You are given a function foo () that represents a biased coin. When foo () is called, it returns 0 with 60% probability, and 1 with 40% probability. Write a new function that returns 0 and 1 with a 50% probability each. Your function should use only foo (), no other library method.

How to make a coin with equal probability?

So the two cases appear with equal probability. The idea is to return consider only the above two cases, return 0 in one case, return 1 in other case. For other cases [ (0, 0) and (1, 1)], recur until you end up in any of the above two cases.

What do you mean by unbiased coin toss?

When we talk about a coin toss, we think of it as unbiased: with probability one-half it comes up heads, and with probability one-half it comes up tails. An ideal unbiased coin might not correctly model a real coin, which could be biased slightly one way or another. After all, real life is rarely fair.

Which is the easiest way to generate a random number?

If b-a is not a power of 2 then you may have to flip many coins in order to get a result. You may even never get a result, but that is unlikely in the extreme. The simplest method is to generate a number in [a, a+2^n), where 2^n >= b-a, until one happens to land in [a, b).