Assume that 3 digits are selected at random from the set {1,3,4,5,6,7}{1,3,4,5,6,7} and are arranged in random order.

What is the probability that the resulting 3-digit number is less than 600?

. In a sequence of 7 Bernoulli trials with probability of success p, let X be the number of successes not followed immediately by a failure. Find E(X) (you can use indicators)

A class has 8 GSIs. Each GSI tosses a coin 20 times and notes the number of heads. What is the probability that none of the GSIs gets exactly 10 heads?

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fractions.

The number of heads in 5 tosses of a coin. Please answer in a table to understand better.

An automotive insurance company wants to predict which filed stolen vehicle claims are fraudulent, based on the mean number of claims submitted per year by the policy holder and whether the policy is a new policy, that is, is one year old or less (coded as 1 = yes, 0 = no). Data from a random sample of 98 automotive insurance claims, organized and stored in InsuranceFraud , show that 49 are fraudulent (coded as 1) and 49 are not (coded as 0). (Data extracted from A. Gepp et al., “A Comparative Analysis of Decision trees vis-à-vis Other Computational Data Mining techniques in Automotive Insurance Fraud Detection,” Journal of Data Science, 10 (2012), pp. 537–561.)

1. Develop a logistic regression model to predict the probability of a fraudulent claim, based on the number of claims submitted per year by the policy holder and whether the policy is new.

2. explain the meaning of the regression coefficients in the model in (a).

3. Predict the probability of a fraudulent claim given that the policy holder has submitted a mean of one claim per year and holds a new policy.

4. At the 0.05 level of significance, is there evidence that a logistic regression model that uses the mean number of claims submit- ted per year by the policy holder and whether the policy is new to predict the probability of a fraudulent claim is a good fitting model?

5. Atthe0.05levelofsignificance,is there evidence that the mean number of claims submitted per year by the policy holder and whether the policy is new each makes a significant contribution to the logistic model?

6. Develop a logistic regression model that includes only the number of claims submitted per year by the policy holder to predict the probability of a fraudulent claim.

7. Develop a logistic regression model that includes only whether the policy is new to predict a fraudulent claim.

8. Compare the models in (a), (f), and (g). evaluate the differences among the models.

In December of 1903, Wilbur and Orville Wright made history with their bi-plane contraption that managed to do the seemingly impossible: it gave man the ability to fly. The concept was so unearthly, in fact, that private aviation first took off not as a means of transportation, but as a sideshow of sorts. In those pioneer days, seeing a man use technology to overcome gravity was such a novelty that early aviators made their living mostly through exhibition flights.

Seven years after the Wright Brothers proved flight was possible, a car salesman by the name of Clyde Cessna found himself awestruck by one such exhibition in Oklahoma. He’d heard tales of men taking to the skies in these machines (and making thousands of dollars in the process), and now that he’d seen one in person he was certain: Clyde Cessna was going to build an airplane of his own.

The Cessna Aviation Company was an American general aviation aircraft manufacturing corporation headquartered in Wichita, Kansas. Cessna produced small, piston-powered aircraft, as well as business jets. For many years the company was one of the highest-volume producers of general aviation aircraft in the world. The company was founded in 1927.

The following information is available concerning a firm's capital:

Debt: 500,000 bonds with a face value of $1000 and an initial 20-year term were issued five years ago with a coupon rate of 8%. Today these bonds are selling for $846.30.

Preferred stock: 200,000 shares of preferred stock paying an annual dividend of $9.50 are outstanding. The shares currently trade at $79.16.

Common equity: Two hundred thousand shares of common stock are outstanding which are now selling for $22.50 per share. An annual dividend of $1.70 was just paid and is expected to grow indefinitely at 6%.

The combined federal and state tax rate is 40%.

Required:

Calculate the firm's WACC.

In the simple distillation of a mixture of toluene and cyclohexane, the average highest temperature recorded was in 95 degrees Celsius. Explain why in the fractional distillation of the same mixture, the average highest temperature was 108 degrees Celsius.

An insurance company has found that 10% of its claims are for damages resulting from burglaries. A random sample of 20 claims is pulled.

a. What is the expected number (mean) that will be claimed for damages resulting from burglaries?

b. What is the standard deviation?

Use Binomial Tables in your text to answer the following:

c. What is the probability that exactly 5 of the 20 will contain claims that are for burglary damages?

d. What is the probability that fewer than 5 will contain claims that are for burglary damages?

e. What is the probability that at least 5 will contain claims that are for burglary damages?

Proportion data follow the binomial distribution, which can be approximated by the normal distribution if np>=5 and nq>=5

True or False?

The sample Proportion p̄=x/n where x is the number of successes and n is the sample size

True or false?

The Type-II error β is the probability of failing to reject a true null Hypothesis Ho.

True or false?

The only way to lower the probability of both errors α and β at the same time, is to decrease the sample size.

True or false?

In Binomial Distribution, If p=40% then the probability of successes is 60%

True or False?