In: Statistics and Probability
A stock's returns have the following distribution:
| Demand for the Company's Products |
Probability of This Demand Occurring |
Rate of Return If This Demand Occurs |
| Weak | 0.1 | (26%) |
| Below average | 0.3 | (8) |
| Average | 0.4 | 15 |
| Above average | 0.1 | 36 |
| Strong | 0.1 | 62 |
| 1.0 |
Assume the risk-free rate is 3%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of variation:
Sharpe ratio:
In: Finance
Use the confusion matrixes to answer the questions below. Record your answers in a word document. Explain your responses and include screen shots where requested. A 5000 row dataset was used to build a model to predict if a person would accept a marketing offer for a personal loan (Personal Loan = Yes). It was partitioned into Training, Validation, and Test with the model results above.
If you were to decrease the cutoff to 0.3 how would that impact your FP and FN counts. Would they increase or decrease? Would your Model Cost increase or decrease?
In: Computer Science
A stock's returns have the following distribution:
| Demand for the Company's Products |
Probability of This Demand Occurring |
Rate of Return If This Demand Occurs |
| Weak | 0.1 | (20%) |
| Below average | 0.3 | (10) |
| Average | 0.4 | 15 |
| Above average | 0.1 | 22 |
| Strong | 0.1 | 74 |
| 1.0 |
Calculate the stock's expected return. Round your answer to two
decimal places.
%
Calculate the stock's standard deviation. Do not round
intermediate calculations. Round your answer to two decimal
places.
%
Calculate the stock's coefficient of variation. Round your answer to two decimal places.
In: Finance
A) An Olympic archer is able to hit the bull’s eye 80% of the time. Assume each shot is independent of the others. She will shoot 6 arrows. Let X denote the number of bull’s eyes she makes.
Find the mean of the probability distribution of X. Do not round
B) The GPA of students at a college has a mean of 2.9 and a standard deviation of 0.3. Scores are approximately normally distributed.
Suppose that the top 6% of students are eligible for the Honors Program. Find the GPA which is the cutoff score for students to qualify for this program. Round to the nearest hundredth.
In: Statistics and Probability
For each of the following cases, determine whether the economy’s labour demand for unskilled workers will decrease or increase:
a) The cross-elasticity of factor demand between unskilled and skilled workers is –0.3, and government implements a policy that results in an increase in demand for skilled workers.
b) The cross-elasticity of factor demand between unskilled workers and capital is 1, and government implements a policy that results in an increase in the demand for capital.
c) The cross-elasticity of factor demand between unskilled and immigrant workers is –1, and government implements a policy that results in an increase in demand for immigrant workers.
In: Economics
A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 17 pipes was taken. The average length in the sample was 15.95 inches with a variance of 0.4 inches.
|
a. |
Construct a 95% confidence interval for the population variance. |
|
b. |
State the null and alternative hypotheses to be tested. |
|
c. |
Compute the test statistic. |
|
d. |
The null hypothesis is to be tested at the 5% level of significance. State the decision rule for the test using the critical value approach. |
|
e. |
What do you conclude about the population variance? |
In: Math
A stock's returns have the following distribution:
| Demand for the Company's Products |
Probability of This Demand Occurring |
Rate of Return If This Demand Occurs |
| Weak | 0.1 | (38%) |
| Below average | 0.1 | (12) |
| Average | 0.4 | 13 |
| Above average | 0.3 | 20 |
| Strong | 0.1 | 47 |
| 1.0 |
Assume the risk-free rate is 3%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of variation:
Sharpe ratio:
In: Finance
For expert using R
I try to solve this question((USING DATA FAITHFUL)) but each time I solve it, I have error , I try it many times. So,everything you write will be helpful..
Modify the EM-algorithm functions to work for a general K component Gaussian mixtures. Please use this function to fit a K= 1;2;3;4 modelto the old faithful data available in R (You need to initialize the EM-algorithm First ).
Which modelseems to t the data better? (Hint: use BIC to compare models.)
Here what I try to use
## EM algorithm for univariate normal mixture
# The E-step
E.step <- function(x, pi, Mu, S2){
K <- length(pi)
n <- length(x)
tau <- matrix(rep(NA, n * K), ncol = K)
for (i in 1:n){
for (k in 1:K){
tau[i,k] <- pi[k] * dnorm(x[i], Mu[k], sqrt(S2[k]))
}
tau[i,] <- tau[i,] / sum(tau[i,])
}
return(tau)
}
#The M-step
M.step <- function(x, tau){
n <- length(x)
K <- dim(tau)[2]
tau.sum <- apply(tau, 2, sum)
pi <- tau.sum / n
Mu <- t(tau) %*% x / tau.sum
S2[1] <- t(tau[,1]) %*% (x - Mu[1])^2 / tau.sum[1]
S2[2] <- t(tau[,2]) %*% (x - Mu[2])^2 / tau.sum[2]
return(list(pi = pi, Mu = Mu, S2 = S2))
}
## The log-likelihood function
logL <- function(x, pi, Mu, S2){
n <- length(x)
ll <- 0
for (i in 1:n){
ll <- ll + log(pi[1] * dnorm(x[i], Mu[1], sqrt(S2[1])) +
pi[2] * dnorm(x[i], Mu[2], sqrt(S2[2])))
}
return(ll)
}
## The algorithm
EM <- function(x, pi, Mu, S2, tol){
t <- 0
ll.old <- -Inf
ll <- logL(x, pi, Mu, S2)
repeat{
t <- t + 1
if ((ll - ll.old) / abs(ll) < tol) break
ll.old <- ll
tau <- E.step(x, pi, Mu, S2)
M <- M.step(x, tau)
pi <- M$pi
Mu <- M$Mu
S2 <- M$S2
ll <- logL(x, M$pi, M$Mu, M$S2)
cat("Iteration", t, "logL =", ll, " ")
}
return(list(pi = M$pi, Mu = M$Mu, S2 = M$S2, tau = tau, logL = ll))
}
## generate data
set.seed(1)
pi <- c(0.3, 0.7)
Mu <- c(5, 10)
S2 <- c(1, 1)
n <- 1000
n1 <- rbinom(1, n, pi[1])
n2 <- n - n1
x1 <- rnorm(n1, Mu[1], sqrt(S2[1]))
x2 <- rnorm(n2, Mu[2], sqrt(S2[2]))
x <- c(x1, x2)
hist(x, freq = FALSE, ylim = c(0, 0.2))
# pick initial values
pi.init <- c(0.5, 0.5)
Mu.init <- c(3, 10)
S2.init <- c(0.4, 2)
#Run EM
A <- EM(x, pi.init, Mu.init, S2.init, tol = 10^-6)
#plot
t <- seq(0, 15, by = 0.01)
y <- pi[1] * dnorm(t, Mu[1], sqrt(S2[1])) +
pi[2] * dnorm(t, Mu[2], sqrt(S2[2]))
y.est <- A$pi[1] * dnorm(t, A$Mu[1], sqrt(A$S2[1])) +
A$pi[2] * dnorm(t, A$Mu[2], sqrt(A$S2[2]))
points(t, y, type = "l")
points(t, y.est, type = "l", col = 2, lty = 2)
# assign observations to components - clustering
d <- function(x) which(x == max(x))
apply(A$tau, 1, d)
apply(A$tau, 1, which.max)
# assess misclassification
table(apply(A$tau, 1, which.max), c(rep(1, n1), rep(2, n2)))
In: Statistics and Probability
The “People” Focus: Human Resources at Alaska Airlines
With thousands of employees spread across nearly 100 locations in the United States, Mexico, and Canada, building a committed and cohesive workforce is a challenge. Yet Alaska Airlines is making it work. The company’s “people” focus states:
While airplanes and technology enable us to do what we do, we recognize this is fundamentally a people business, and our future depends on how we work together to win in this extremely competitive environment. As we grow, we want to strengthen our small company feel . . . We will succeed where others fail because of our pride and passion, and because of the way we treat our customers, our suppliers and partners, and each other.
Managerial excellence requires a committed workforce. Alaska Airlines’ pledge of respect for people is one of the key elements of a world-class operation.
Effective organizations require talented, committed, and trained personnel. Alaska Airlines conducts comprehensive training at all levels. Its “Flight Path” leadership training for all 10,000 employees is now being followed by “Gear Up” training for 800 front-line managers. In addition, training programs have been developed for Lean and Six Sigma as well as for the unique requirements for pilots, flight attendants, baggage, and ramp personnel. Because the company only hires pilots into first officer positions—the right seat in the cockpit, it offers a program called the “Fourth Stripe” to train for promotion into the captain’s seat on the left side, along with all the additional responsibility that entails (see exterior and interior photos of one of Alaska Airlines’ flight simulators on the opening page of this chapter).
Customer service agents receive specific training on the company’s “Empowerment Toolkit.” Like the Ritz-Carlton’s famous customer service philosophy, agents have the option of awarding customers hotel and meal vouchers or frequent flier miles when the customer has experienced a service problem.
Because many managers are cross-trained in operational duties outside the scope of their daily positions, they have the ability to pitch in to ensure that customer-oriented processes go smoothly. Even John Ladner, Director of Seattle Airport Operations, who is a fully licensed pilot, has left his desk to cover a flight at the last minute for a sick colleague.
Along with providing development and training at all levels, managers recognize that inherent personal traits can make a huge difference. For example, when flight attendants are hired, the ones who are still engaged, smiling, and fresh at the end of a very long interview day are the ones Alaska wants on the team. Why? The job requires these behaviors and attitudes to fit with the Alaska Airlines team—and smiling and friendly flight attendants are particularly important at the end of a long flight.
Visual workplace tools also complement and close the loop that matches training to performance. Alaska Airlines makes full use of color-coded graphs and charts to report performance against key metrics to employees. Twenty top managers gather weekly in an operations leadership meeting, run by Executive VP of Operations, Ben Minicucci, to review activity consolidated into visual summaries. Key metrics are color-coded and posted prominently in every work area.
Alaska’s training approach results in empowered employees who are willing to assume added responsibility and accept the unknowns that come with that added responsibility.
Discussion Questions*
In: Operations Management