Question 1

Expected value represents
A) the actual payment one expects to receive.
B) the average of all payments one would receive if one undertook the risky event many times.
C) the payment one receives if he or she makes the correct decision.
D) the payment that is most likely to occur.

Accepted Answer

The expected value represents the average of all payments one would receive if one undertook the risky event many times. It takes into account all possible outcomes and their probabilities to determine the average outcome. It is not necessarily the actual payment one expects to receive, the payment one receives if he or she makes the correct decision, or the payment that is most likely to occur.

Question 2

If a payout is certain to occur,then the variance of that payout equals
A) zero.
B) one.
C) the expected value.
D) the expected value squared.

Accepted Answer

If a payout is certain to occur, then there is no uncertainty, and hence no possibility of variability in the payout. Therefore, the variance would be zero.

Question 3

On any given day we know a salesman can earn $0 with a 40% probability,$100 with a 20% probability or $300 with 40% probability.His expected earnings equal
A) $0.
B) $140.
C) $300.
D) It cannot be determined from the available information.

Accepted Answer

The expected earnings can be calculated as:

(0.4 * 0) + (0.2 * 100) + (0.4 * 300) = 0 + 20 + 120 = 140

Therefore, the expected earnings of the salesman is $140.

Question 4

On any given day,a salesman can earn $0 with a 20% probability,$100 with a 40% probability,or $300 with a 20% probability.His expected earnings equal
A) $0.
B) $100 because that is the most likely outcome.
C) $100 because that is what he will earn on average.
D) $200 because that is what he will earn on average.

Accepted Answer

The expected earnings are calculated by multiplying each outcome by its probability and summing these products: (0 * 0.20) + (100 * 0.40) + (300 * 0.20) = 0 + 40 + 60 = $100.

Question 5

Your friend Diana tells you that she thinks that her favorite softball team has a 70% chance of winning the next game because that is exactly the winning rate of her team in the last two seasons.This is an example of a(n)
A) objective probability.
B) subjective probability.
C) risk-averse statement.
D) Friedman-Savage preference.

Accepted Answer

The answer of Your friend Diana tells you that she...

Question 6

On any given day,a salesman can earn $0 with a 30% probability,$100 with a 20% probability,or $300 with a 50% probability.His expected earnings equal
A) $0.
B) $100.
C) $150.
D) $170.

Accepted Answer

The expected earnings can be calculated by taking the probability-weighted average of the possible earnings, which gives:
Expected earnings = (0.30 x $0) + (0.20 x $100) + (0.50 x $300) = $0 + $20 + $150 = $170
Therefore, the salesman's expected earnings are $170. The best choice is (D).

Question 7

People in a certain group have a 0.3% chance of dying this year.If a person in this group buys a life insurance policy for $3,300 that pays $1,000,000 to her family if she dies this year and $0 otherwise,what is the expected value of a policy to the insurance company?
A) $0
B) $300
C) $3,000
D) $3,300

Accepted Answer

The expected value is calculated by multiplying the possible outcomes by their respective probabilities and adding them together. In this case, there are two possible outcomes: the policyholder dies and the insurance company pays out $1,000,000 or the policyholder does not die and the insurance company pays out $0. The probability of the policyholder dying is 0.3%, or 0.003. Therefore, the expected value is:

(0.003 * $1,000,000) + ((1 - 0.003) * $0) = $3,000
The policy is sold for $3,300, so the expected value to the insurance company is negative $300. This means that on average, the insurance company can expect to lose $300 for every policy sold. Therefore, the best choice is B, as it represents the expected value to the insurance company.

Question 8

A share of a restaurant chain can be worth $2 with a probability of 0.40 and $10 with a probability of 0.60.What is the variance of the price of this share?
A) 3
B) 5
C) 6
D) 8.5

Accepted Answer

The expected value (E) is calculated as: E = (0.40 * $2) + (0.60 * $10) = $7. The variance is calculated as: Variance = (0.40 * ($2 - $7)^2) + (0.60 * ($10 - $7)^2) = 6.

Question 9

You draw colored balls out of a bag.You draw a red ball 30% of the time and a blue ball 70% of the time.For each draw,the blue outcome and the red outcome are
A) mutually exclusive.
B) exhaustive.
C) Both A and B.
D) None of the above.

Accepted Answer

The outcomes of drawing a red ball and drawing a blue ball are mutually exclusive because you cannot draw both a red ball and a blue ball at the same time. Additionally, they are exhaustive because one must either draw a red ball or a blue ball. Therefore, the best choice is C, both A and B.

Question 10

If there are 10,000 people in your age bracket,and 10 of them died last year,an insurance company believes that the probability of someone in that age bracket dying this year would be
A) 0.
B) .001.
C) .0001.
D) 1,000.

Accepted Answer

The probability of someone in the age bracket dying this year can be calculated by dividing the number of people who died last year by the total number of people in the age bracket:
 
Probability = Number of deaths last year / Total number of people in the age bracket
Probability = 10 / 10,000
Probability = 0.001
 
Therefore, the probability of someone in the age bracket dying this year is 0.001 or 0.1%.

Question 11

Lauren noticed that in the last 60 games,her hometown minor league baseball team won 40 times.Lauren estimate the probability of losing the game to be
A) 1/6.
B) 1/4.
C) 1/3.
D) 1/2.

Accepted Answer

The team lost 20 out of 60 games, so the probability of losing is 20/60 = 1/3.

Question 12

Expected value represents the average of all outcomes if one were to undertake the risky event many times over and over again.

Accepted Answer

The expected value is not expected on any one outcome,because it represents the average of many outcomes.

Question 13

A share of an oil company can be worth $10 with a probability of 0.50 and $20 with a probability of 0.50.What is the standard deviation of the price of this share?
A) 3
B) 5
C) 6
D) 8.5

Accepted Answer

To calculate the standard deviation, we need to first calculate the expected value (or mean) of the share price:

Expected value = (0.5 * $10) + (0.5 * $20) = $15

Then, we can calculate the variance:

Variance = [(0.5 * ($10 - $15)^2) + (0.5 * ($20 - $15)^2)] = $25

Finally, we take the square root of the variance to get the standard deviation:

Standard deviation = sqrt($25) = $5

Therefore, the answer is B - 5.

Question 14

Assume the following.In location A yearly temperatures range from -30°F to 100°F and in location B yearly temperatures range from 55°F to 75°F.In both locations the average yearly temperature equals 65°F.We can conclude that
A) temperature in location A has a higher variance.
B) temperature in location B has a higher standard deviation.
C) temperature in location A has a lower standard deviation.
D) temperatures in both locations have the same standard deviation but different variances.

Accepted Answer

Variance measures the spread of a set of numbers. Location A, with a wider range of temperatures from -30°F to 100°F, exhibits a greater spread compared to Location B's narrower range of 55°F to 75°F. Therefore, Location A has a higher variance, and since standard deviation is the square root of variance, it also implies a higher standard deviation for Location A.

Question 15

Sarah buys little stuffed animals for $5 each.They come in different varieties.If the producer stops making (retires)a certain variety,a stuffed animal of that variety will be worth $100; otherwise it is worth $0.There is 50% chance that any variety will be retired.When Sarah buys her next stuffed animal,the expected profit is
A) $50.
B) $47.50.
C) $45.00.
D) $0.

Accepted Answer

The answer of Sarah buys little stuffed animals for $5...

Question 16

Your friend Dimitre tells you that he thinks that his favorite basketball team has a 70% chance of winning the next game.This is an example of a(n)
A) objective probability.
B) subjective probability.
C) risk-averse statement.
D) Friedman-Savage preference.

Accepted Answer

Dimitre's statement is an example of subjective probability because it is based on his personal belief or opinion rather than on any actual data or calculation. Objective probability, on the other hand, is based on empirical evidence or historical data. The other options (C and D) are not relevant to the given statement.

Question 17

Although he is very poor,Al plays the million-dollar lottery every day because he is certain that one day he will win.Al makes this calculation based upon
A) the frequency of past outcomes.
B) subjective probability.
C) knowledge of all possible outcomes.
D) tossing a coin.

Accepted Answer

Al's belief that he will win the lottery is not based on any objective or historical data, so A and C can be eliminated. It is also not a random event where he has a 50/50 chance of winning like tossing a coin, so D can also be eliminated. Therefore, the best choice is subjective probability as he has developed a personal belief that he will eventually win, despite the low odds of winning.

Question 18

A lottery game pays $500 with .001 probability and $0 otherwise.The variance of the payout is
A) 15.8.
B) 249.50.
C) 249.75.
D) 499.

Accepted Answer

The variance of a discrete probability distribution can be found using the formula:
Var(X) = Σ [ (xi - μ)^2 * P(xi) ]
where xi is the payout for each possible outcome, μ is the expected payout, and P(xi) is the probability of each outcome.

In this case, we have two possible outcomes:
- $500 with probability 0.001
- $0 with probability 0.999

So we can calculate the expected payout as:
E(X) = $500 * 0.001 + $0 * 0.999 = $0.50

Using the formula for variance, we get:
Var(X) = (500 - 0.5)^2 * 0.001 + (0 - 0.5)^2 * 0.999
Var(X) = 249.75

Therefore, the best choice is C.

Question 19

All else held constant,as the variance of a payoff increases,the
A) expected value of the payoff increases.
B) risk of the payoff increases.
C) expected value of the payoff decreases.
D) risk of the payoff decreases.

Accepted Answer

Variance is a measure of dispersion or spread of the values in a distribution. Therefore, as the variance of a payoff increases, it indicates a greater possibility of the actual returns deviating from the expected value. This increases the risk associated with the payoff. As a result, option B is correct.

Question 20

Sarah buys little stuffed animals for $5 each.They come in different varieties.If the producer stops making (retires)a certain variety,a stuffed animal of that variety will be worth $100; otherwise it is worth $0.There is 50% chance that any variety will be retired.What is the value to Sarah of knowing ahead of time whether a variety will be retired?
A) $50
B) $5
C) $2.50
D) $0

Accepted Answer

The value of knowing ahead of time is calculated as the difference between the expected value with and without the information. Without the information, the expected value of a stuffed animal is 0.5 * $100 + 0.5 * $0 = $50. With the information, the value is either $100 (if retired) or $0 (if not), but since she would only buy the retired ones, her expected value is $100. The value of the information is $100 - $50 = $50. However, since she pays $5 for each stuffed animal, the net value to Sarah of knowing ahead of time is $50 - $5 = $45. This option is not listed, indicating a misunderstanding in the explanation process. The correct interpretation should focus on the expected gain from the decision to buy or not buy based on the information, which is the increase in expected value due to having the information. Given the options, the closest correct approach to understanding the value of the information is by considering how it affects the decision-making process in terms of expected outcomes, which seems to have been misinterpreted in the initial explanation.

Quiz 17: Uncertainty

Expected value represents

If a payout is certain to occur,then the variance of that payout equals

On any given day we know a salesman can earn $0 with a 40% probability,$100 with a 20% probability or $300 with 40% probability.His expected earnings equal

On any given day,a salesman can earn $0 with a 20% probability,$100 with a 40% probability,or $300 with a 20% probability.His expected earnings equal

Your friend Diana tells you that she thinks that her favorite softball team has a 70% chance of winning the next game because that is exactly the winning rate of her team in the last two seasons.This is an example of a(n)

On any given day,a salesman can earn $0 with a 30% probability,$100 with a 20% probability,or $300 with a 50% probability.His expected earnings equal

People in a certain group have a 0.3% chance of dying this year.If a person in this group buys a life insurance policy for $3,300 that pays $1,000,000 to her family if she dies this year and $0 otherwise,what is the expected value of a policy to the insurance company?

A share of a restaurant chain can be worth $2 with a probability of 0.40 and $10 with a probability of 0.60.What is the variance of the price of this share?

You draw colored balls out of a bag.You draw a red ball 30% of the time and a blue ball 70% of the time.For each draw,the blue outcome and the red outcome are

If there are 10,000 people in your age bracket,and 10 of them died last year,an insurance company believes that the probability of someone in that age bracket dying this year would be

Lauren noticed that in the last 60 games,her hometown minor league baseball team won 40 times.Lauren estimate the probability of losing the game to be

Expected value represents the average of all outcomes if one were to undertake the risky event many times over and over again.

A share of an oil company can be worth $10 with a probability of 0.50 and $20 with a probability of 0.50.What is the standard deviation of the price of this share?

Assume the following.In location A yearly temperatures range from -30°F to 100°F and in location B yearly temperatures range from 55°F to 75°F.In both locations the average yearly temperature equals 65°F.We can conclude that

Your friend Dimitre tells you that he thinks that his favorite basketball team has a 70% chance of winning the next game.This is an example of a(n)

Although he is very poor,Al plays the million-dollar lottery every day because he is certain that one day he will win.Al makes this calculation based upon

A lottery game pays $500 with .001 probability and $0 otherwise.The variance of the payout is

All else held constant,as the variance of a payoff increases,the