Random Variables and Distributions

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.

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

A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?

• 0.20
• 0.29
• 0.39
• 0.61

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

• $12.50
• $5
• $7.50
• $10

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. What is the expected value of a ticket?

• lose an average of $5.50
• lose an average of $1.50
• win an average of $2.00
• lose an average of $10.00