Question
Asked Mar 14, 2019
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Consider the game of craps designed by Econ 261 Hotel students. The game consists of rolling two fair six-sided dice. You win a dollar if the sum of the dots on the two dice is 2, 3, 4, or 5; if the sum of the dots on the two dice is 9, 10, 11, or 12 you lose a dollar. You win nothing, (that is you get $0) if the sum is 6, 7, or 8. The variance of X, Var(X) is what?

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Expert Answer

Step 1

Find the sample space:

Here, the game designed by Econ hostel students consists of rolling two fair six sided dice.

Sample space:

The set of all possible outcomes of a probability experiment is called sample space of the experiment.

Here, two fair dice are rolled.

The total number of outcomes in the sample space be n(S) = 62 = 36. That is, there will be 36 equally likely outcomes.

Outcomes will be occurred in ordered pairs. First number in each ordered pair represents the number on the first die and second number in each ordered pair represents the number on the second die. Each of the two numbers can take values 1 to 6.

The sum of the numbers on the dice will be 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

The sample space for the experiment is given below:

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Step 2

Find the outcomes that match the desired requirement:

The outcomes in favor of the event of getting the sum of dice as 2, 3, 4 or 5:

The outcomes in the event of getting the sum of dice as 2, 3, 4 or 5 consist of all the possible outcomes for the sum of the dice to be 2, 3, 4 and 5.

The number of outcomes in favor of the event of getting the sum of dice as 2, 3, 4 or 5 is 10.

The outcomes in favor of the event of getting the sum of dice as 9, 10, 11 or 12:

The outcomes in the event of getting the sum of dice as 9, 10, 11 or 12 consist of all the possible outcomes for the sum of the dice to be 9, 10, 11 and 12.

The number of outcomes in favor of the event of getting the sum of dice as 9, 10, 11 or 12 is 10.

The outcomes in favor of the event of getting the sum of dice as 6, 7 or 8:

The outcomes in the event of getting the sum of dice as 6, 7 or 8 consist of all the possible outcomes for the sum of the dice to be 6, 7 and 8.

The number of outcomes in favor of the event of getting the sum of dice as 6, 7 or 8 is 16.

The total number of outcomes is 36.

The probability of an event is obtained as,

P = (number of favorable events)/(total number of events)

Step 3

Conditions to construct a probability distribution table:

Discrete random variable:

If the variable X takes finite or countable values, then the variable X is said to be discrete.

Conditions for the discrete probability distribution:

  • The proba...

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