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Which of the following could least likely be a probability function?

A) X1,2,3,4) p(x) = 0.2.

B) X1,2,3,4) p(x) = (x × x) / 30.

C) X1,2,3,4) p(x) = x / 10.

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In a probability function, the sum of the probabilities for all of the outcomes must equal one. Only one of the probability functions in these answers fails to sum to one.

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A probability function:

A) is often referred to as the "cdf."

B) specifies the probability that the random variable takes on a specific value.

C) only applies to continuous distributions.

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This is true by definition.

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A random variable that has a countable number of possible values is called a:

A) probability distribution.

B) continuous random variable.

C) discrete random variable.

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A discrete random variable is one for which the number of possible outcomes are countable, and for each possible outcome, there is a measurable and positive probability. A continuous random variable is one for which the number of outcomes is not countable.

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Which of the following is least likely to be an example of a discrete random variable?

A) The rate of return on a real estate investment.

B) The number of days of sunshine in the month of May 2006 in a particular city.

C) Quoted stock prices on the NASDAQ.

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The rate of return on a real estate investment, or any other investment, is an example of a continuous random variable because the possible outcomes of rates of return are infinite (e.g., 10.0%, 10.01%, 10.001%, etc.). Both of the other choices are measurable (countable).

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Assume a discrete distribution for the number of possible sunny days in Provo, Utah during the week of April 20 through April 26. For this discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can. Based on this information, what is the probability of it being sunny on 5 days and on 10 days during the week, respectively?

A) A positive value; infinite.

B) A positive value; zero.

C) Zero; infinite.

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The probability of it being sunny on 5 days during the week has some positive value, but the probability of having sunshine 10 days within a week of 7 days is zero because this cannot occur.

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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.

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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.

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Which of the following is a discrete random variable?

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

B) The realized return on a corporate bond.

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

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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.

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

A) Indiscrete.

B) Continuous.

C) Discrete.

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

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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) 0.001.

B) 0.167.

C) 0.200.

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

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A probability distribution is least likely to:

A) contain all the possible outcomes.

B) give the probability that the distribution is realistic.

C) have only non-negative probabilities.

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The probability distribution may or may not reflect reality. But the probability distribution must list all possible outcomes, and probabilities can only have non-negative values.