Reading 9: Common Probability Distributions - LOS j ～ Q1-5 black, class

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1、The farthest point on the left side of the lognormal distribution:

A)   is bounded by 0.

B)   can be any negative number.

C)   cannot be determine with the information given.

D)   is skewed to the left.

2、Given Y is lognormally distributed, then ln Y is:

A)   a lognormal distribution.

B)   normally distributed.

C)   the antilog of Y.

D)   indeterminate.

3、If random variable Y follows a lognormal distribution then the natural log of Y must be:

A)   lognormally distributed.

B)   denoted as e^x.

C)   abnormally distributed.

D)   normally distributed.

4、If a random variable x is lognormally distributed then ln x is:

A)   abnormally distributed.

B)   the antilog of x.

C)   defined as e^x.

D)   normally distributed.

5、Which of the following statements regarding the distribution of returns used for asset pricing models is most correct?

A)   Normal distribution returns are used for asset pricing models because they will only allow the asset price to fall to zero.

B)   Normal distribution returns are used for asset pricing models because lognormal returns result in spurious results.

C)   Lognormal distribution returns are used for asset pricing models because they will not result in an asset return of less than -100%.

D)   Lognormal distribution returns are used because this will allow for negative returns on the assets.

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答案和详解如下：

1、The farthest point on the left side of the lognormal distribution:

A)   is bounded by 0.

B)   can be any negative number.

C)   cannot be determine with the information given.

D)   is skewed to the left.

The correct answer was A)

The lognormal distribution is skewed to the right with a long right hand tail and is bounded on the left hand side of the curve by zero.

2、Given Y is lognormally distributed, then ln Y is:

A)   a lognormal distribution.

B)   normally distributed.

C)   the antilog of Y.

D)   indeterminate.

The correct answer was B)

If Y is lognormally distributed, then ln Y is normally distributed.

3、If random variable Y follows a lognormal distribution then the natural log of Y must be:

A)   lognormally distributed.

B)   denoted as e^x.

C)   abnormally distributed.

D)   normally distributed.

The correct answer was D)

For any random variable that is lognormally distributed its natural logarithm (ln) will be normally distributed.

4、If a random variable x is lognormally distributed then ln x is:

A)   abnormally distributed.

B)   the antilog of x.

C)   defined as e^x.

D)   normally distributed.

The correct answer was D)

For any random variable that is normally distributed its natural logarithm (ln) will be lognormally distributed. The opposite is also true: for any random variable that is lognormally distributed its natural logarithm (ln) will be normally distributed.

5、Which of the following statements regarding the distribution of returns used for asset pricing models is most correct?

A)   Normal distribution returns are used for asset pricing models because they will only allow the asset price to fall to zero.

B)   Normal distribution returns are used for asset pricing models because lognormal returns result in spurious results.

C)   Lognormal distribution returns are used for asset pricing models because they will not result in an asset return of less than -100%.

D)   Lognormal distribution returns are used because this will allow for negative returns on the assets.

The correct answer was C)    

Lognormal distribution returns are used for asset pricing models because this will not result in asset returns of less than 100% because the lowest the asset price can decrease to is zero which is the lowest value on the lognormal distribution. The normal distribution allows for asset prices less than zero which could result in a return of less than -100% which is impossible.