2. A player pays $3 to play the following game: He rolls a die and receives...

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

here let net winnning is X.

below is pmf of X:

P(X=7-3=4) =P(rolling a 6)=1/6

P(X=1-3=-2)=P(rolling other number than 6)=5/6

therefore from above:

expected net winning E(X) = $\sum$ xP(x) =4*(1/6)-2*(5/6)= $ -1

E(X²)= $\sum$ x²P(x) =4²*(1/6)+(-2)²*(5/6)= 6

therefore standard deviation =sqrt(E(X²)-E(X)²) =sqrt(6-1²) =sqrt(5)=$ 2.236

Answer 2

Similar Homework Help Questions

A player pays $4 to play the following game: He tosses three fair coins and receives...

A player pays $4 to play the following game: He tosses three fair coins and receives back “payoff” of $1 if he tosses no heads, $2 for one head, $4 for 2 heads, and $6 for 3 heads.Find the player’s expected net winnings for this game.
In a game of repeated die rolls, a player is allowed to roll a standard die...

In a game of repeated die rolls, a player is allowed to roll a standard die up to n times, where n is determined prior to the start of the game. On any roll except the last, the player may choose to either keep that roll as their final score, or continue rolling in hopes of a higher roll later on. If the player rolls all n times, then after the nth roll, the player must keep that roll as...
Consider a play of the casino game `Quick Draw'. In this game, a player pays $11...

Consider a play of the casino game `Quick Draw'. In this game, a player pays $11 to play. The player picks one card from a standard pack of 52 cards (i.e. there are four A’s and four K’s in a standard pack of 52 cards). If the player gets an Ace, they win $50 but loose the amount they paid to play (the profit is revenue minus cost); if the player selects a King, they win $30 but loose the...

for a game you pay 2$ to play and roll 1 die. If the number is...

for a game you pay 2$ to play and roll 1 die. If the number is a 1 or 2 you win 9$. If the number is a 6, you win 3$. If the number is anything else, you receive nothing. FInd the expected value (the fair price to charge to play).
3. Player 1 and Player 2 are going to play the following stage game twice: &n...

3. Player 1 and Player 2 are going to play the following stage game twice: Player 2 Left Middle Right Player 1 Top 4, 3 0, 0 1, 4 Bottom 0, 0 2, 1 0, 0 There is no discounting in this problem and so a player’s payoff in this repeated game is the sum of her payoffs in the two plays of the stage game. (a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1...

A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1 head occurs and $1 if no heads occur. () Find his expected to play the game if it is to be fair? winnings. ) How much should he pay

Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1,...

Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives Alyssa $5. If Alyssa rolls a 4 or 5, Gabriel gives Alyssa $4. However, if Alyssa rolls a 6, she gives Gabriel $24. a) Determine Alyssa's expectation. b) Determine Gabriel's expectation.
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the...

4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks onē card from the standard deck of 52 cards (i.e. four A's, four K's, etc.). If the player selects an "A", he/she wins $50 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. Let the...
A dice game is played as follows: The "buy-in" to play a round costs $4. Then...

A dice game is played as follows: The "buy-in" to play a round costs $4. Then a fair 6-sided die is rolled and the player receives an equal number of dollars as the number shown on the die (i.e. 1 earns $1, 2 earns $2, etc.). What is the player's expected profit from playing one round of the game? -$0.25 $0.25 O-$1.00 -$0.50 Page 4 of 34 Dronnie Dace Next Pare

In a dice game, the player independently rolls a fair red die and a fair green...

In a dice game, the player independently rolls a fair red die and a fair green die.The player wins if and only if the red die shows a 1, or 2, or 3, or if the total on the two dice is 11. What is the probability the player will win?