Probabilities in a coin-one thousand tossing experiment

Question

Explain an example of probabilities in a simple coin-tossing experiment one thousand tosses.

Answer 1

Probabilities in a simple coin-tossing experiment: one thousand tosses

Now here’s what your total profit will be like after one thousand tosses as in figure. Therefore expected profit after one toss is

(1/6) x 10 + (5/6) x (-1) = 5/6 ≈ 0.833

Standard deviation is therefore

√(1,000 x (605/54)) ≈ 34.7

Notice how the standard deviation has grown much less than the hope. That’s due to the square-root rule. In finance we frequently assume that equity all returns are normally distributed. We could argue here, this ought to be the case by saying such that returns over any finite period, one day, say that are made up of many, several trades over smaller time periods, along with the result as the returns over the finite timescale are normal thanks to the Central Limit Theorem.