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Is the Gaussian Bell Curve time dependent?

Suppose we toss a coin and depending on the outcome we win or lose one dollar. If we do it for a long time (infinity), the outcome when plotted will resemble a Gaussian Bell Curve. Now if the action (tossing of coin) is spread across time, like say, 10 flips on day 1, 10 flips on day 3, 10 flips on day 9 and so on, will it have a effect on the distribution (all other conditions remaining the same). Logically, as per me, it should not, theoretically - but in reality is it probable?

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Mar 20 at 6:23
  • $\begingroup$ My question is in the beginning - Is Gaussian Bell Curve time dependents. The remaining are explanations to the above query. $\endgroup$
    – Tamoghna Paul
    Mar 20 at 6:31
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    $\begingroup$ Hint: In the game you describe the total profit or loss does not depend on when you tossed the coin. $\endgroup$
    – Kurt G.
    Mar 20 at 6:33

1 Answer 1

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While a Gaussian bell curve is not intrinsically time dependent, it is possible that the distribution of outcomes over longer periods of time may deviate from the expected result due to changes in conditions or external factors. For instance, if the coin used at different times is slightly different (e.g., one side is lighter than the other), this could affect the outcome and skew results away from those predicted by a Gaussian bell curve. Similarly, external variables such as environmental conditions or subtle changes in technique during tossing can also influence results over time. Thus, while you may expect to see a stable Gaussian bell curve across short-term experiments, it is best to consider all potential factors when predicting outcomes over longer periods.

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