Which of the two options is better, or are they the same? Explainbriefly. (i) Yo

Question

Which of the two options is better, or are they the same? Explainbriefly.
(i) You toss a coin 100 times. On each toss, if the coin landsheads, you win $1. If it lands tails, you lose $1.
(ii) You draw 100 times at random with replacementfrom 0 1 . On each draw, you are paid (in dollars)the number on the ticket.

Any help would be greatly appreciated!
(i) You toss a coin 100 times. On each toss, if the coin landsheads, you win $1. If it lands tails, you lose $1.
(ii) You draw 100 times at random with replacementfrom 0 1 . On each draw, you are paid (in dollars)the number on the ticket.

Any help would be greatly appreciated!

Explanation / Answer

To answer this question we must simply compute the expected valuesof the two scenarios. The expected value of the first scenario is obviously 0. There is a .5 chance it will land heads and a .5 chance it willland tails. The expected number of heads is therefore50. If you have 50 heads and 50 tails, you make exactly$0. The expected value of the second one is different however. You are drawing with replacement, so it is as if you make the samedrawing 100 times. As you are selecting from a uniform 0, 1distribution, the expected value of each drawing is $.5 The expected value of 100 draws therefore is .5(100) =$50. Obviously, $50 is better than $0, so you would prefer thesecond.

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