Each round of game played by a gambler is either a win with probability p or...

Each round of game played by a gambler is either a win with probability p or a loss with probability 1 − p. If the round is a win, then a random amount of money having an exponential distribution with rate λ will be awarded to the gambler. If the round is a loss, then he loses everything that had been accumulated up to that time and cannot play any additional rounds. After a win round, the gambler can either choose to quit and keep whatever has been won or can choose to play another round. Suppose that a gambler plans to continue playing until either his total winnings exceeds t or a loss occurs.

(a) What is the expectation of N, the number of winning rounds that it would take until his fortune 1 exceeds t?

(b) What is the probability he will successfully reach a fortune of at least t?

Expert Solution

milcah answered 1 day ago

In a certain game it is possible to win either 1,2,3,4, or 5 dollars. The probability...

In a certain game it is possible to win either 1,2,3,4, or 5 dollars. The probability of winning d dollars is proportional to 1/d. (a) What is the probability of winning d dollars (d ∈{1,2,3,4,5})? (b) Would you play this game for $4? What about for $3? Hint. You must calculate the expected value for this problem! (c) What is the variance of the expected winnings of this game?

If you played this game 619 times how much would you expect to win or lose?

Suppose a basketball player has made 233 out of 303free throws. If the player makes the next 3 free throws, I will pay you $7. Otherwise you pay me $8Step 2 of 2 : If you played this game 619 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

In a gambling game, on every play, there is a 0.1 probability that you win $7...

In a gambling game, on every play, there is a 0.1 probability that you win $7 and a 0.9 probability that you lose $1. What is the expected value of this game?

On each bet, a gambler loses $2 with probability 0.2, loses $1 with probability 0.7, or...

On each bet, a gambler loses $2 with probability 0.2, loses $1 with probability 0.7, or wins $10 with probability 0.1. After 100 of these bets, what is the approximate probability that the gambler's total is negative? Show your work below.

The probability that a certain hockey team will win any given game is 0.3628 based on...

The probability that a certain hockey team will win any given game is 0.3628 based on their 13 year win history of 377 wins out of 1039 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November. Find the probability that the hockey team wins at least 7 games in November. (Round your answer to four decimal places.) Please use TI-84 calculator not excel. Thanks!

In the casino game roulette, the probability of winning with a bet on red is p...

In the casino game roulette, the probability of winning with a bet on red is p = 17/38. Let Y equal the number of winning bets out of 1000 independent bets that are placed. Find P(Y > 500), approximately. Show all your work.

Monshimout is a game from the Cheyenne people and played by women. It could be played...

Monshimout is a game from the Cheyenne people and played by women. It could be played by two or more players, and if played by more than two, then the players divided into two equal teams. Game equipment consisted of five plum stones and a basket made of woven grass or willow twigs. The basket measured 3-4 inches deep, 8 inches across at the top, and almost 1/2 inch thick. The plum stones were left plain on one side, but...

3.The “Guess-the Mean Game” is played as follows: Each of the N players writes on a...

3.The “Guess-the Mean Game” is played as follows: Each of the N players writes on a piece of paper an integer between 1 and 10 without showing it to any other players. The players then reveal the numbers they have written down. The winner is that person whose number comes the closest to equaling half the average of the number submitted by the other players. For example, if there are four players and they write down the numbers 1, 3,...

A game is played as follows. There are 2 goats and 1 car, each hidden behind...

A game is played as follows. There are 2 goats and 1 car, each hidden behind a numbered door. You choose a door (for simplicity you always choose door 1) and then Monty Hall opens one of doors 2 or 3.The door that he opens always reveals a goat. Now Monty offers you to switch yourchoice of doors (a) What is the probability that you win the car by switching your choice? Hint: Consider the events {Ci= car is behind...

1. A round in the game Yahtzee begins by rolling five fair dice. Find the probability...

1. A round in the game Yahtzee begins by rolling five fair dice. Find the probability of rolling a: a. one pair (ex 33421 but not 33441), two pair (ex 33441 but not 33444), and three of a kind (ex 24252 but not 24242) 2. Consider a 10x10 matrix that consists of all zeros. ten elements of the matrix are selected at random and their value is changed from a zero to a one. find the probability that the ones...

Question