Q6. A dealer in a casino has rolled a five on a single die three times in a row. What is the probability of her rolling another five on the next roll, assuming it is a fair die?

A)   0.167.

B)   0.001.

C)   0.200.

Q7. The number of ships in the harbor is an example of what kind of variable?

A)   Discrete.

B)   Indiscrete.

C)   Continuous.

Q8. Which of the following is a discrete random variable?

A)     The realized return on a corporate bond.

B)     The amount of time between two successive stock trades.

C)     The number of advancing stocks in the DJIA in a day.

Q9. Which of the following statements about probability distributions is most accurate?

A)   A discrete uniform random variable has varying probabilities for each outcome that total to one.

B)   A binomial distribution counts the number of successes that occur in a fixed number of independent trials that have mutually exclusive (i.e. yes or no) outcomes.

C)   A continuous uniform distribution has a lower limit but no upper limit.

答案和详解如下：

Q6. A dealer in a casino has rolled a five on a single die three times in a row. What is the probability of her rolling another five on the next roll, assuming it is a fair die?

A)   0.167.

B)   0.001.

C)   0.200.

Correct answer is A)

The probability of a value being rolled is 1/6 regardless of the previous value rolled.

Q7. The number of ships in the harbor is an example of what kind of variable?

A)   Discrete.

B)   Indiscrete.

C)   Continuous.

Correct answer is A)

A discrete variable is one that is represented by finite units.

Q8. Which of the following is a discrete random variable?

A)     The realized return on a corporate bond.

B)     The amount of time between two successive stock trades.

C)     The number of advancing stocks in the DJIA in a day.

Correct answer is C)

Since the DJIA consists of only 30 stocks, the answer associated with it would be a discrete random variable. Random variables measuring time, rates of return and weight will be continuous.

Q9. Which of the following statements about probability distributions is most accurate?

A)   A discrete uniform random variable has varying probabilities for each outcome that total to one.

B)   A binomial distribution counts the number of successes that occur in a fixed number of independent trials that have mutually exclusive (i.e. yes or no) outcomes.

C)   A continuous uniform distribution has a lower limit but no upper limit.

Correct answer is B)

Binomial probability distributions give the result of a single outcome and are used to study discrete random variables where you want to know the probability that an exact event will happen. A continuous uniform distribution has both an upper and a lower limit. A discrete uniform random variable has equal probabilities for each outcome.

thank you

Q1. Ryan McKeeler and Howard Hu, two junior statisticians, were discussing the relation between confidence intervals and hypothesis tests. During their discussion each of them made the following statement:

McKeeler: A confidence interval for a two-tailed hypothesis test is calculated as adding and subtracting the product of the standard error and the critical value from the sample statistic. For example, for a level of confidence of 68%, there is a 32% probability that the true population parameter is contained in the interval.

Hu: A 99% confidence interval uses a critical value associated with a given distribution at the 1% level of significance. A hypothesis test would compare a calculated test statistic to that critical value. As such, the confidence interval is the range for the test statistic within which a researcher would not reject the null hypothesis for a two-tailed hypothesis test about the value of the population mean of the random variable.

With respect to the statements made by McKeeler and Hu:

A)   both are correct.

B)   only one is correct.

C)   both are incorrect.

Correct answer is B)

McKeeler’s statement is incorrect. Specifically, for a level of confidence of say, 68%, there is a 68% probability that the true population parameter is contained in the interval. Therefore, there is a 32% probability that the true population parameter is not contained in the interval. Hu’s statement is correct.

Q2. Given a mean of 10% and a standard deviation of 14%, what is a 95% confidence interval for the return next year?

A)   -17.44% to 37.44%.

B)   -4.00% to 24.00%.

C)   -17.00% to 38.00%.

Correct answer is A)

10% +/- 14(1.96) = -17.44% to 37.44%.

谢谢哦