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AIM 7: Distinguish between univariate and multivariate probability density functions.

1、Which of the following would least likely be categorized as a multivariate distribution?

A) The days a stock traded and the days it did not trade.

B) The return of a stock and the return of the DJIA.

C) The days a stock traded and the days the DJIA went up.

D) The returns of the stocks in the DJIA.

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The correct answer is A

The number of days a stock traded and did not trade describes only one random variable. All the other cases involve two or more random variables

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2、A multivariate distribution:

A) gives multiple probabilities for the same outcome.

B) applies only to normal distributions.

C) applies only to binomial distributions.

D) specifies the probabilities associated with groups of random variables.

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The correct answer is D

This is the definition of a multivariate distribution.

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3、In a multivariate normal distribution, a correlation tells the:

A) strength of the linear relationship between two of the variables.

B) overall relationship between all the variables.

C) relationship between the means and variances of the variables.

D) relationship between the means and standard deviations of the variables.

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The correct answer is A

This is true by definition. The correlation only applies to two variables at a time.

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AIM 9: Explain the difference between statistical independence and statistical dependence.

1、If X and Y are independent events, which of the following is most accurate?

A) P(X or Y) = P(X) + P(Y).

B) X and Y cannot occur together.

C) P(X | Y) = P(X).

D) P(X or Y) = (P(X)) × (P(Y)).

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The correct answer is C

Note that events being independent means that they have no influence on each other. It does not necessarily mean that they are mutually exclusive. Accordingly, P(X or Y) = P(X) + P(Y) ? P(X and Y). By the definition of independent events, P(X|Y) = P(X).

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2、A company says that whether its earnings increase depends on whether it increased its dividends. From this we know:

A) P(both dividend increase and earnings increase) = P(dividend increase).  

B) P(earnings increase | dividend increase) is not equal to P(earnings increase). 

C) P(dividend increase or earnings increase) = P(both dividend and earnings increase). 

D) P(dividend increase | earnings increase) is not equal to P(earnings increase). 

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The correct answer is B

If two events A and B are dependent, then the conditional probabilities of P(A|B) and P(B|A) will not equal their respective unconditional probabilities (of P(A) and P(B), respectively). The other choices may or may not occur, e.g., P(A | B) = P(B) is possible but not necessary.