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.(a) suppose you play roulette and bet $3 on a single round. what is the expected value and standard deviation of your total winnings? (b) suppose you bet $1 in three dierent rounds. what is the expected value and standard deviation of your total winnings? (c) how do your answers to parts (a) and (b) compare? what does this say about the riskiness of the two games?

a) E(X) = -$0.0813 , s.d (X) = 3

b) E(X) = -$0.0813 , s.d (X) = 3

c) expected loss and higher stakes of loosing.

Step-by-step explanation:

Given:

- There are total 37 slots:

           Red = 18

           Black = 18

           Green = 1

- Player on bets on either Red or black

- Wins double the bet money, loss the best is lost

Find:

a) Expected value of earnings X if we place a bet of $3

b) Expected value and standard deviation if we bet $1 each on three rounds

c) compare the two answers in a and b and comment on the riskiness of the two games

Solution:

- Define variable X as the total winnings per round. We will construct a distribution tables for total winnings per round for bets of $3 and $ 1:

- Bet: $3

         X                   -3                          3                              E(X)

        P(X)           1-0.48 = 0.5135      18/37 = 0.4864    3*(.4864-.52135) = -0.08

-The s.d(X) = sqrt(9*(0.5135 + 0.4864) - (-0.08)^2) = 3.0

- Bet: $1

         X                   -1                          1                          E (X)      

        P(X)        1-0.48 = 0.5135      18/37 = 0.4864   1*(.4864-.5135) = -0.0271

-The s.d(X) = sqrt(1*(0.5135 + 0.4864) - (-0.0271)^2) = 0.999

- The expected value for 3 rounds is:

                       E(X_1 + X_2 + X_3) = E(X_1) + E(X_2) + E(X_3)

- The above X winnings are independent from each round, hence:

                       E(3*X_1) = 3*E(X_1) = 3*(-0.0271) = -0.0813

- The standard deviation for 3 rounds is:

              sqrt(Var(X_1 + X_2 + X_3)) = sqrt(Var(X_1) + Var(X_2) + Var(X_3))

- The above X winnings are independent from each round, hence:

                       sqrt(Var(3*X_1)) = 3*Var(X_1) = 3*(0.999) = 2.9988

- For above two games are similar with an expected loss of $0.0813 for playing the game and stakes are very high due to high amount of deviation for +/- $3 of winnings.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.