Time preferences
I loan you $5,000 today, with the understanding that you will give me back $10,000 in ten years. In 10 years, what is the future value of this gift at 5% interest rate? Am I getting a good return on my investment?
The future value of the loan is $8,144, since I'm getting $10,000 I'm getting a higher rate of return.
BONUS: What is the rate of return that I'm actually getting?n
If a board has 12 members, how many ordered president-vp-secretary combinations can be chosen?
1320
12! / (12-3)!
If 60% of students like chocolate, 40% like mint, but only 30% like both. What is the probability that, if a student tells you they like mint, that they ALSO like chocolate?
75%
P(c&m) = P (c <intersect>m) / P(m)
If a bear on average stores 50 pounds of berries, with a standard deviation of 5 pounds, what is the approximate probability that a randomly selected bear will be found with between 42 and 60 pounds of berries? (USE CHEBYSHEVS)
At least 60.9%
-- Use Chebyshev's with X+/-8 to take the more conservative range.
Explain the key assumptions for a Binomial distribution and Poisson distribution?
Binomial - fixed n; y/n per trail; independence between trials; same probability across trials
Poisson - same prob across intervals (average rate); independent across intervals; rare occurrence
If you want to have $500,000 for retirement in 10 years, what do you need to put into an account now, assuming a constant interest rate of 4%?
$337,998 is the amount you need to invest now (PV)
I have a coin that I flip three times. What is the probability of tossing a heads at least once and a tails at least once?
75% or 6/8
P = 1- P(all heads or all tails) = 1 - (2/8) = 6/8
If 60% of students like chocolate, 40% like mint, but only 30% like both, what is the probability that a randomly selected student likes either chocolate OR mint? Are these preferences mutually exclusive?
70% like both -- no they're not mutually exclusive
A particular species of flower can either bloom red or blue. 70% of flowers bloom red. If I have 10 flowers that are ready to bloom, what is the probability that exactly five will bloom red?
10.3%
A nutrition researcher is studying the relationship between daily hours of exercise (X) and weekly calories burned (Y)among adults. From a sample of 30 people, she finds: Variance of exercise hours is 1.44; Variance of calories burned is 90000; Covariance between exercise hours and calories burned is 330. Calculate the correlation coefficient (r) between hours of exercise and calories burned.
pxy = 0.917, which means there's a strong positive linear relationship -- when you excercise more per day, you burn more calories per week
You take out a loan for $50,000 today for a Ferrari -- nice. If you want to have to recoup the full value of the loan in 7 years, what do you need to pay each year, assuming a discount rate of 3% with payments at the start of each year?
$7,790 paid at the start of each year
P(A) and P(B) must be independent and mutually exclusive
On a given night 10% of the populations is drunk. A new test correctly detects drunken-ness 95% of the time, but also yields false-positives 4% of the time. If your test tells you someone is drunk, what is the probability that they actually are?
72.5% that if the test says you're drunk, you actually are!
On average, a bookstore sells 3 rare books per day. What is the probability that will sell exactly 15 books in a given week? What are your assumptions?
3.95%, assumes constant rate throughout the week, independent events
Explain the difference between a sample and a population. How do these impact formulas you might use to understand their mean, variance and stdv?
[OWEN TO EXPLAIN]
What is the present value of a payment of $40 a year that starts in 5 years and goes forever, assuming a discount rate of 5%?
A password must consist of 4 different letters chosen from the 26 letters of the alphabet. How many possible 4-letter passwords can be made if no letters are repeated?
358,800 possible four-letter passwords
An email spam filter classifies messages as “spam” or “not spam". 20% of all incoming emails are actually spam. The filter correctly identifies spam emails 95% of the time. However, it mistakenly classifies 2% of legitimate (not spam) emails as spam. What is the probability that an email is actually spam if it is marked as spam?
92.2%
The time (in minutes) that customers spend waiting in line at a coffee shop is uniformly distributed between 3 and 15 minutes. What is the average wait time? What is the likelihood that you have to wait for more than 8 minutes?
Wait of more than 8 mins is about 58.3% (7/12)
You invest in two stocks, A and B. 40% of your money is in Stock A; 60% of your money is in Stock B
From past data, Stock A’s variance (how much its returns vary) is 0.0225 and Stock B’s variance is 0.0400 and the correlation between the two stocks is 0.30. What is the variance of your total portfolio’s return?
0.149
I'm giving you $1000 a month for the next 5 years, starting at the end of this year. Assume an interest rate of 7%. What is the present value of this gift?
It's worth ~$50,570 today
(r = 0.07/12 =0.00583 per month)
(n = 5 * 12 = 60 months)
I have two 9-sided dice. What is the probability of rolling at least one odd number AND at least one number more than six?
~46.9% or 38/81
P(odd & >6) = 1 - ( P(even) + P(<6) - P(even & <6)
P (even) = 16/81
P(<6) = 36/81
P (even & <6) = 9/81
There are three breweries in town, L & M & N. L makes up 60% of the market, but 2% of their beer is flat. M is 30% and 1%. N is 10% and 5%. If I am drinking a flat beer, what is the probability it came from N?
25% chance the beer is from N
The weights of coffee bags produced by a machine are normally distributed with a mean of 500 grams and a standard deviation of 8 grams. What is the probability that a randomly selected bag weighs less than 484 grams or more than 516 grams? What percentage of bags fall within those bounds (between 484 g and 516 g)?
4.56% (2*P(Z>2))
1-above = 95.44%
You and four friends are in a class together. Project groups are five people. The total class is 50 students, including you. What is the chance that, given groups are selected by the teacher at random, you will be in the same group with all your friends (e.g., they will fill the remaining 4 seats in your group)?
0.000472%
There is 1 good outcome where the remaining four seat (k=4) are filled by your four friends (n=4), out of a large number of combinations where the remaining for seats (k=4) across the 49 other students (n=49)