aianjie

 

3、A major securities exchange is considering the introduction of a new derivative contract. In the past, the success rate for new derivatives has been 30 percent. Extensive market research has produced a positive marketing research report for the contract under consideration. Historically, 70 percent of the successful contracts have received favorable reports prior to introduction. Only 10 percent of unsuccessful contracts have received favorable reports. What is the probability that the new contract will be successful?

A) 87%.

B) 75%.

C) 13%.

D) 25%.

aianjie

 

The correct answer is B

Let S denote success, U denote unsuccessful, and F denote a favorable report. We have P(S)=0.30, P(U)=0.70, P(F | S)=0.70, and P(F | U)=0.10. Using Bayes theorem, the probability of a successful contract, given a favorable report is:[attach]13843[/attach]

 

 

aianjie

 

AIM 5: Define probability mass function, probability function, probability density function, cumulative distribution function.

Which of the following statements about probability distributions is least accurate?

A) In a binomial distribution each observation has only two possible outcomes that are mutually exclusive.

B) A probability distribution is, by definition, normally distributed.

C) A probability distribution includes a listing of all the possible outcomes of an experiment.

D) One of the key properties of a probability function is  0 ≤ p ≤ 1.

aianjie

 

The correct answer is B

Probabilities must be zero or positive, but a probability distribution is not necessarily normally distributed. Binomial distributions are either successes or failures.

aianjie

 

AIM 6: Discuss the implications the normal probability density function has.

1、A normal distribution can be completely described by its:

A) skewness and kurtosis.

B) mean and mode. 

C) mean and variance. 

D) standard deviation.

aianjie

 

The correct answer is C

The normal distribution can be completely described by its mean and variance.

aianjie

 

2、The lower limit of a normal distribution is:

A) negative infinity.

B) zero.

C) one.

D) negative one.

aianjie

 

The correct answer is A

By definition, a true normal distribution has a positive probability density function from negative to positive infinity.

aianjie

 

3、Which of the following statements about a normal distribution is least accurate?

A) A normal distribution has excess kurtosis of three.

B) The mean, median, and mode are equal.

C) The mean and variance completely define a normal distribution.

D) Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.

aianjie

 

The correct answer is A

Even though normal curves have different sizes, they all have identical shape characteristics. The kurtosis for all normal distributions is three; an excess kurtosis of three would indicate a leptokurtic distribution. The other choices are true.