Reading 9: Common Probability Distributions LOS b习题精选 2010, specified, possible, through

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LOS b: Describe the set of possible outcomes of a specified discrete random variable.

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; zero.

B) A positive value; infinite.

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

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

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

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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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.