Random Variables Practice

Which of the following is not a random variable?

• The heights of randomly-selected buildings in New York City.
• The suit of a card randomly-selected from a 52-card deck.
• The number of children in randomly-selected households in the United States.
• The amount of money won (or lost) by the next person to walk out of a casino in Las Vegas.

A random variable is

• a hypothetical list of the possible outcomes of a random phenomenon.
• any phenomenon in which outcomes are equally likely.
• any number that changes in a predictable way in the long run.
• a variable whose value is a numerical outcome associated with a random phenomenon.

I roll a pair of fair dice and let X =  the sum of the spots on the two sides facing up.  The probability that X is 2, 11, or 12 is

• 1/36
• 2/36
• 3/36
• 4/36

In a particular game, a fair die is tossed.  If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing.  Let X be the amount that you win. 
Which of the following is the expected value of X?

• $1.00
• $2.50
• $4.00
• $6.00

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day.  Based on the records, X has the following probability distribution.
The mean number of customers that make a purchase during the first hour that the store is open is:
   

• 2.0
• 2.5
• 2.9
• 3

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day.  Based on the records, X has the following probability distribution.
The standard deviation of the number of customers that make a purchase during the first hour that the store is open is

• 0.2
• 1.4
• 2.0
• 3.0

The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g is

• .1056
• .3944
• .1042
• .8944

Your friend Albert has invented a game involving two ten-sided dice.  One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens.  He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then μ_x=3.6, σ_x=0.8, μ_y=8.0 and σ_y=0.9. Let Z = the sum of the two dice when each is rolled once.
What is the expected value of Z?

• 1.7
• 4.4
• 5.8
• 11.6

Your friend Albert has invented a game involving two ten-sided dice.  One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens.  He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then μ_x=3.6, σ_x=0.8, μ_y=8.0 and σ_y=0.9. Let Z = the sum of the two dice when each is rolled once. 
What is the standard deviation of Z?

• 1.20
• 1.30
• 1.45
• 1.70

Your friend Albert has invented a game involving two ten-sided dice.  One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens.  He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then μ_x=3.6, σ_x=0.8, μ_y=8.0 and σ_y=0.9. Let Z = the sum of the two dice when each is rolled once. 
Here's Albert's game: You give him $10 each time you roll, and he pays you (in dollars) the amount that comes up on the dice.  If P = the amount of money you gain each time you roll, the mean and standard deviation of P are:

• μ_P=-1.6; σ_P=1.45
• μ_P=1.6; σ_P=1.45
• μ_P=1.6; σ_P=1.2
• μ_P=-1.6; σ_P=13.8