The current 1-year spot rate on a treasury bill is 4.25% and the current 1-year spot rate on a BB-rated bond of equivalent risk to a prospective loan is 11.55%. The bond has a marginal probability of default in year 2 of 8.5% 11. What is the marginal probability of default in year 1? (3 points) 12. What is the cumulative probability of default over the 2 years? (4 points)
In: Finance
Over the last 5 years a region has been hit by an average of 5 tornadoes per year. Assume this figure to be accurate and that the probability of a tornado occurring remains constant throughout a year. Calculate
a) The probability that the same area will be hit by at least 4 tornadoes this year.
b) The probability more than 4 months go by without a tornado.
The answer below for a) and b) in order separated by a comma is one of the following.
In: Statistics and Probability
5. The occurrence of traffic accidents at an intersection is
modeled as a Poisson process. Based on accident records at that
intersection, a traffic engineer has determined that the average
rate of accidents occurring at that intersection is once every
three years.
(a) What is the probability that no accident occurs at that
intersection for a period of 5 years?
(b) What is the probability that there is a traffic fatality at
that intersection over a period of 3 years if for every accident
there is 5% probability of fatality?
In: Statistics and Probability
Using the table below, find the Probability of Ordering as a decimal and percent. Please show your work and formulas you would use in excel.
| # of pizzas ordered | # of customers who ordered | Probability of ordering (decimal value) | Probability of ordering (as a percent) |
| 1 | 8 | ||
| 2 | 9 | ||
| 3 | 6 | ||
| 4 | 1 | ||
| 5 | 0 | ||
| 6 | 0 | ||
| 7 | 0 | ||
| 8 | 0 | ||
| Sum total | 24 |
In: Statistics and Probability
Given maturities of 1,2- and 20-year bonds with respective yields of 4, 5 and 11 percent. These bonds have rated yields at 7, 9, and 16 percent.What is the implied probability of repayment on one-year B-rated debt? What is B-rated debt bonds and implied probability represent here? Show work and discuss the importance of implied probability.
MUST SHOW WORK. PLEASE AND THANK YOU!
In: Finance
A company is considering drilling oil wells. The probability of success for each well is 0.20. The cost of each well is $5 (in1000). Each well that is successful will be worth $60 (in 1000).
1) If the company drills 4 wells, the probability of at least one successful well is
2) If the company drills 40 wells, the approximate probability of at most one successful well is
3) The expected profit and the variance of profit in 4 drillings are
In: Statistics and Probability
A football receiver, Harvey Gladiator, is able to catch two thirds of the passes thrown to him. He must catch four passes for his team to win the game. The quarterback throws the ball to Harvey six times. (a) Find the probability that Harvey will drop the ball all six times. (b) Find the probability that Harvey will win the game. (c) Find the probability that Harvey will drop the ball at least two times.
In: Math
6. Consider the probability distributions of hydrogen angular states. (a) (5 pts) For what values of θ is the angular probability density maximum and minimum for l = 1, m = 0? (b) (5 pts) For what values of θ is the angular probability density maximum and minimum for l = 3, m = ±1? This may be difficult to do analytically, so make a plot with your computer, or simply sketch the function
In: Physics
In: Statistics and Probability
In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.
Do you take the free samples offered in supermarkets? About 56% of
all customers will take free samples. Furthermore, of those who
take the free samples, about 42% will buy what they have sampled.
Suppose you set up a counter in a supermarket offering free samples
of a new product. The day you were offering free samples, 323
customers passed by your counter. (Round your answers to four
decimal places.)
(a) What is the probability that more than 180 will take your
free sample?
(b) What is the probability that fewer than 200 will take your free
sample?
(c) What is the probability that a customer will take a free sample
and buy the product? Hint: Use the multiplication rule for
dependent events. Notice that we are given the conditional
probability P(buy|sample) = 0.42, while P(sample)
= 0.56.
(d) What is the probability that between 60 and 80 customers will
take the free sample and buy the product? Hint:
Use the probability of success calculated in part (c).
In: Statistics and Probability