Random Variables

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

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.2

CCSS.HSS.MD.B.5

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

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.2

Cool TV game show

Players win prizes with probabilities shown:

P($0) = .70

P($500) = .25

P($5,000) = .05

What are the mean and the standard deviation of the prize variable?

• Mu = $375; sigma = $361

• Mu = $375; sigma = $1,083

• Mu = $1,833; sigma = $1,816

• Inadequate info is provided.

Tags

CCSS.HSF-LE.A.1B

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise.  What is the expected amount you win?

• $0.00
• -$1.00
• $1.00
• $3.00

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.2

CCSS.HSS.MD.B.5

Is the distribution below a probability distribution? Why or why not?

• Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1
• No, not all P(x) values are between 0 and 1.
• No, ∑P(x) ≠ 1.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.1

CCSS.HSS.MD.A.4

Identify whether the experiment involves a discrete or a continuous random variable.

Collecting data about the mileage per liter of a certain brand and model of a car

• Discrete Random Variable

• Continuous Random Variable

Identify whether the experiment involves a discrete or a continuous random variable.

tossing a pair of fair coins

• Discrete Random Variable

• Continuous Random Variable

Identify whether the experiment involves a discrete or a continuous random variable.

Recording the number of points scored by a NBA team in each game of the 2018 season

• Discrete Random Variable

• Continuous Random Variable

Identify whether the experiment involves a discrete or a continuous random variable.

Number of phone calls answered by a call center agent during his/her shift

• Discrete Random Variable

• Continuous Random Variable

Tags

CCSS.HSS.MD.A.1

Identify whether the experiment involves a discrete or a continuous random variable.

Measuring the length of time it takes before a dolphin surfaces in the ocean to breath

• Discrete Random Variable

• Continuous Random Variable