What type of PMF was used to solve this problem - geometric,binomial, etc... for

Question

What type of PMF was used to solve this problem - geometric,binomial, etc... for this problem. Suppose you go to a casino with exactly $63. You playroulette with only red and green. P(red) = P(green) =1/2. First bet is $1, if you win you walk away with$64. If you loose you double down with $2, then if youwin you walk away. If you loose you be $4, and so on, untilyou win or run out of money. Let Y = the amount of money you takehome. Find PY(y) and E[Y]. I have theanswer, but need to explain how I got there. What type of PMF was used to solve this problem - geometric,binomial, etc... for this problem. Suppose you go to a casino with exactly $63. You playroulette with only red and green. P(red) = P(green) =1/2. First bet is $1, if you win you walk away with$64. If you loose you double down with $2, then if youwin you walk away. If you loose you be $4, and so on, untilyou win or run out of money. Let Y = the amount of money you takehome. Find PY(y) and E[Y]. I have theanswer, but need to explain how I got there.

Explanation / Answer

This is a geometric PMF. Let's just analyze the question. So basically, you keepplaying roulette until you win. That is very similar to acommon geometric probability question of you roll a die until youroll a 3. (or you keep flipping a coin until headsappears). Therefore, you can just use the geometric formulas (should bein your textbook) to find Py(y) and E[y].

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