Problem 4: Stock prices Adnan, a 16-year old teenager, has invested an initial amount Yo = 1000$ on the WIN stock. The WIN stock behaves quite bizarrely. Every day, the amount invested by Adnan either doubles in value or is halved. This happens completely randomly and independently of other days. In other words, if we define X1,...,X, to be independent and identically distributed random variables taking on value 2 with probability 1/2 and value 1/2 with probability 1/2, we can write Y., the amount that Adnan has after n days as Y = X, Y,- for all n > 1, that is the amount he had the previous day, multiplied by a random variable that indicates whether the stock's price has halved or doubled. Adnan's parents think that he should not be investing money at his age on the stock market. They have struck up the following deal with him: if he gets to 100,000$, they will acknowledge they were wrong and take him out for a meal; if he goes below 208, he will have to make them dinner for the next month. Who is most likely to win the bet? How soon can Adnan and his parents expect the bet to be resolved? Problem 4: Stock prices Adnan, a 16-year old teenager, has invested an initial amount Yo = 1000$ on the WIN stock. The WIN stock behaves quite bizarrely. Every day, the amount invested by Adnan either doubles in value or is halved. This happens completely randomly and independently of other days. In other words, if we define X1,...,X, to be independent and identically distributed random variables taking on value 2 with probability 1/2 and value 1/2 with probability 1/2, we can write Y., the amount that Adnan has after n days as Y = X, Y,- for all n > 1, that is the amount he had the previous day, multiplied by a random variable that indicates whether the stock's price has halved or doubled. Adnan's parents think that he should not be investing money at his age on the stock market. They have struck up the following deal with him: if he gets to 100,000$, they will acknowledge they were wrong and take him out for a meal; if he goes below 208, he will have to make them dinner for the next month. Who is most likely to win the bet? How soon can Adnan and his parents expect the bet to be resolved