Any math or probabilty geniuses out there?

Question

If you flip a coin, heads is + 1 and tails is - 1. I need to know the maximum + and - you can expect over 1000 flips, and also the average deviation from 0 that you can expect. Thanks for the help

Thank you for the answers. I'm looking for the likely results and not whats possible.

Anubhav2k- Just don't answer the question if you don't know the answer. Easy enough.

Answer 1

For 1000 flips, the "standard deviation" from 500 of the number of heads (or tails) is plus or minus sqrt(250), which is just under 16. And the mathematical shape of the distribution is "binomial", but for such a big number of flips it is indistiguishable from a "Gaussian" or "normal" distribution.

So about 68% of the time your score (for heads +1, tails -1) should be between -16 and 16. About 95% of the time it will be between -32 and 32. There is only a 0.3% chance that it will be outside of -48 to 48.

Answer 2

The maximum is 1000 and the minimum is -1000, both cases occuring when every flip is identical, a very unlikely situation. The 1000 flips constitute 1000 independent variables, which means that you would get a normal distribution, an important mathematical result; a large number of independent variables always produces the normal distribution for numerical values. When you say "average deviation," I assume you mean "standard deviation." With a maximum of 1000 and a minumum of -1000, it can be approximated that 1000 is equivalent to three standard deviations. In a true normal distribution, there is no maximum or minimum, but the probability of falling outside three standard deviations is about 0.3%. If 1000 is three standard deviations, 333 is one standard deviation.

Answer 3

It is about root(1000)
The average is zero.

Th

Answer 4

when you ask question, please state the level of question so that we could answer you according to the level of question because each question has merit according to the class or standard