NORMAL DISTRIBUTION
Which of the following statements is true about the normal random walk model, Y[t] = Y[t-1] + e[t], where e[t] is a normal shock
... [Show More] with
mean zero and standard deviation sigma?
-This random walk model depends upon the initial state of the system.
-Each shock is independent of all prior shocks.
Which of the following is true of the normal distribution model? Select all correct answers.
-The normal distribution has "thin tails" because large outliers are unlikely to occur.
-The area under a normal density curve represents probability.
-The normal distribution originated as an approximation to the binomial distribution.
-It is a family of bell-shaped density curves, each with a different mean and standard deviation.
-Phenomena that don’t look obviously normal can be sometimes described using the normal distribution as a building block.
-Observing a normal random variable more than three standard deviations beyond its expected value is an unlikely, rare event.
-The area under a normal density curve represents probability.
The normal distribution would be an appropriate probability model in which of the following contexts?
-As an approximation for a large-N binomial model
A formula that defines each term in a sequence using the preceding terms in that sequence is said to be:
-recursive
The national weather service collects annual data for the Austin metropolitan area. Of the following, which is a continuous random
variable?
-Annual rain accumulation
Which of the following are correct statements about "for" loops and "do" loops in R?
-"do" loops allow us to repeat a calculation or simulation many times, as long as we don't require that the results of one simulation can affect the
results of another simulation.
-A "for" loop will always have a "counting" or "iterator" variable.
-"For" loops are useful for chaining the results of computations together, with the result of one computation feeding into the next computation.
Probability Models
A manufacturer of video game controllers is concerned that their controller may be difficult for left-handed users. Suppose that 22% of the population is lefthanded. Consider a sample of 12 customers. Can the number of left-handed gamers in the sample be modeled as a Binomial random variable?
-Yes, if we assume that each customer has a 22% chance of being left-handed.
Which of the following is a discrete random variable?
-The number of customers waiting in line at Franklin BBQ when it opens tomorrow morning.
-The count of typos on a page.
Approximately 8% of males are color blind. Consider a random sample of 25 men.
Which of the following are among assumptions we make in modeling the number of color blind males in the sample as a Binomial random variable?
-Knowing that one member of the sample is color-blind (or not) does not change the probability that any other member of the sample is color-blind (or not).
-We are observing a fixed number of random events (i.e., each person in the sample).
-Each random event may be considered as a "yes" or a "no".
Which of the following is a continuous random variable?
-The high temperature in Austin today.
Suppose that you have a house worth $200,000, and that there is a 1 in 23,021 chance that your home will experience a flood this year. Suppose that, if a flood
happens, there's a 90% chance that it will cause partial damage worth $20,000, and a 10% chance that it will total your house (i.e. cause $200,000 worth of
damage). What is the expected value of flood damage to your house this year? Round your answer to two decimal places (i.e. to the nearest penny).
-(1/23021)*(.9*20000)+(1/23021)*(.1*200000)=1.65
Hoping to compete with the likes of Amazon Web Services and Microsoft Azure in the competitive cloud computing market, software-as-a-service provider
Nimbus 2K has bid on a major contract.
There is a 15% chance the firm wins the contract and earns a profit of $1,000,000
There is a 10% chance the firm wins the contact but with higher expenses, earning a profit of $750,000
Otherwise, the firm loses the contact and they earn no profit.
The expected value of the contract profit for Nimbus 2K is:
-((0.10)*750000)+((0.15)*1000000) = $225,000 [Show Less]