Random Variables

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.

The number of school lunches sold during the month. 

• Discrete

• Continuous

A child asks his parents for some money. The parents make the following offers.
 Father’s offer: The child fl ips a coin. If the coin lands heads up, the father will give the child $20. If the coin lands tails up, the father will give the child nothing.
Mother’s offer: The child rolls a 6-sided die. The mother will give the child $3 for each dot on the upside of the die.
Which offer has the greater expected value?

• Mother's Offer

• Father's Offer

The standard deviation of X is σ_X=1.08 where X represents the number of cars for a household. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

• The mean number of cars would be about 1.08

• The number of cars would typically vary by about 1.08 from the mean

• The number of cars would be at most 1.08 from the mean

• the number of cars would be within 1.08 from the mean about 68% of the time

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.

C & C Partners is planning a major investment, The amount of profit X (millions of dollars) is uncertain, but an estimate gives the following probability distribution. Profit 1 1.5 2 4 10 Probaibility .1 .2 .4 .2 .13 Based on this estimate, mean of X = 3 and standard deviation is 2.52. C & C Partners owes its lenders $200,000 and 10% of the profits X. So the firm actually retains Y = 0.9X -.2 from the investment. Find the mean and standard deviation of Y.

• Mean 2.5 Standard deviation = 2.68

• Mean -2.7 Standard deviation =2.268

• Mean = 2.5 Standard deviation = 2.268

• Mean 2.8 Standard deviation = 2.068

Fernando is 60 inches tall. The average height for his age and gender is 68 with a standard deviation of 10 inches. What percent of his peers are shorter than him?

• 46.81%

• 8%

• 78.81%

• 21.19%

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8? 

• 81.85%

• 47.5%

• 68%

• 95%

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

Suppose that a detailed study has revealed that for romance novels the number of pages has mean 364 and standard deviation of 47, and that for detective novels the number of pages has mean 404 and standard deviation 173.  A reader is going to select at random one romance novel, independently selected at random one detective novel and read both book. What is the standard deviation of the total number of pages the person will read? 

• 14.8

• 110.0

• 179.3

• 220.0