Expected value in multiple rounds
I am doing an exercise that sounds like:
The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.
First question is:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
I created this table to solve it:
Where I got SD = 2.14 and Expected value = -0.09
However the second question I don't know what to do:
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
Can I just do E(X) * 3?
probability statistics random variance standard-deviation
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
add a comment |
I am doing an exercise that sounds like:
The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.
First question is:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
I created this table to solve it:
Where I got SD = 2.14 and Expected value = -0.09
However the second question I don't know what to do:
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
Can I just do E(X) * 3?
probability statistics random variance standard-deviation
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
add a comment |
I am doing an exercise that sounds like:
The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.
First question is:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
I created this table to solve it:
Where I got SD = 2.14 and Expected value = -0.09
However the second question I don't know what to do:
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
Can I just do E(X) * 3?
probability statistics random variance standard-deviation
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
I am doing an exercise that sounds like:
The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.
First question is:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
I created this table to solve it:
Where I got SD = 2.14 and Expected value = -0.09
However the second question I don't know what to do:
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
Can I just do E(X) * 3?
probability statistics random variance standard-deviation
probability statistics random variance standard-deviation
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
asked Nov 29 '18 at 10:21
StudentCoderJavaStudentCoderJava
678
678
add a comment |
add a comment |
1 Answer
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Guide:
Number the rounds $1,2,3$ and write: $$X=X_1+X_2+X_3$$ where $X_i$ denotes the winning in round $i$ for $i=1,2,3$.
Apply linearity of expectation to find $mathbb EX$.
Realize that the $X_i$ are independent and use the rule: $$mathsf{Var}(U+V)=mathsf{Var}(U)+mathsf{Var}(V)$$ for independent random variables $U,V$ for which variance is defined.
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Guide:
Number the rounds $1,2,3$ and write: $$X=X_1+X_2+X_3$$ where $X_i$ denotes the winning in round $i$ for $i=1,2,3$.
Apply linearity of expectation to find $mathbb EX$.
Realize that the $X_i$ are independent and use the rule: $$mathsf{Var}(U+V)=mathsf{Var}(U)+mathsf{Var}(V)$$ for independent random variables $U,V$ for which variance is defined.
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
add a comment |
Guide:
Number the rounds $1,2,3$ and write: $$X=X_1+X_2+X_3$$ where $X_i$ denotes the winning in round $i$ for $i=1,2,3$.
Apply linearity of expectation to find $mathbb EX$.
Realize that the $X_i$ are independent and use the rule: $$mathsf{Var}(U+V)=mathsf{Var}(U)+mathsf{Var}(V)$$ for independent random variables $U,V$ for which variance is defined.
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
add a comment |
Guide:
Number the rounds $1,2,3$ and write: $$X=X_1+X_2+X_3$$ where $X_i$ denotes the winning in round $i$ for $i=1,2,3$.
Apply linearity of expectation to find $mathbb EX$.
Realize that the $X_i$ are independent and use the rule: $$mathsf{Var}(U+V)=mathsf{Var}(U)+mathsf{Var}(V)$$ for independent random variables $U,V$ for which variance is defined.
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
Guide:
Number the rounds $1,2,3$ and write: $$X=X_1+X_2+X_3$$ where $X_i$ denotes the winning in round $i$ for $i=1,2,3$.
Apply linearity of expectation to find $mathbb EX$.
Realize that the $X_i$ are independent and use the rule: $$mathsf{Var}(U+V)=mathsf{Var}(U)+mathsf{Var}(V)$$ for independent random variables $U,V$ for which variance is defined.
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
answered Nov 29 '18 at 10:39
drhabdrhab
98.4k544129
98.4k544129
add a comment |
add a comment |
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