Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n2 if heads comes up rst on the nth toss. If we play this game repeatedly, how much money do you expect to win or lose per game over the long run

$4

Explanation:

A geometric distribution is commonly known as a probability distribution that is used for the total number of Bernoulli trials computed till there is a successful trial. Therefore:

If X is the toss with the first head, then, it is a geometric distribution with p = 0.5. The payable amount (A) will be:

= (1+0.5)/(0.5)^2 = 1.5/0.25 = 6

If $10 is used to play the game, the loss will be 10-6 = $4 per game.

cognitive overload: having a lot on your mind impairs decision-making and tends to result in the simplest, but not necessarily best, option being selected.

empathy gaps: overlooking how you might feel in a different situation can result in unnecessary purchases, such as overbuying when shopping for food on an empty stomach.

optimism and overconfidence: wearing rose-tinted glasses and having unrealistic expectations about the future can affect money management and leave you unprepared for a change in circumstance.

instant gratification: seeking instant gratification drives impulsive spending and can undermine long-term planning and savings.

harmful habits: automatic or mindless behaviour can amplify a poor financial decision as it becomes a recurring event.

social norms: we are heavily influenced by the actions of others; while this can be in certain circumstances, it also contributes to the pressure to keep up with the joneses through conspicuous consumption.

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