Exam 5: Discrete Probability Distributions

A random variable is a function that assigns numerical values to the outcomes of a random experiment.

A consumer who is risk neutral is best characterized as ______________.

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.What is the probability that at least 1 of the expectant mothers will have a Caesarean delivery?

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.What is the standard deviation of the number of mothers who will have a Caesarean delivery?

During an hour of class,a professor anticipates six questions on average. A)What is the probability that in a given hour of class,exactly six questions are asked? B)What is the expected number of questions asked in a 20-minute period? C)What is the probability that no questions are asked over a 20-minute period?

A six-sided,unfair (weighted)die has the following probability distribution. Find the probability of rolling a 3 or less.

A risk averse consumer ignores risk and makes his/her decisions solely on the basis of expected value.

Exhibit 5-12.According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics,May,2011).Eight working-age residents were chosen at random. Refer to Exhibit 5-12.What is the probability that exactly four residents were unemployed?

Which of the following can be represented by a continuous random variable?

In a particular game of cards,success is measured by the number of aces drawn by each player.Eight cards are drawn by the first player.Given that the player is drawing from a full poker deck of 52 cards,find the probability that this player will draw two aces from the deck.

Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period?

Exhibit 5-11.For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11.What is the probability that at least two of the customers redeem the coupon?

Exhibit 5-4.Consider the following probability distribution. Refer to Exhibit 5-4.The expected value is _____.

You are attending a baseball game with two family members when it is announced that four fans in your section (which holds 20 spectators total)will win a free autographed baseball. A)What is the probability that at least one member in your family (including yourself)wins an autographed baseball? B)What is the probability that exactly two members of your family win an autographed baseball? C)What is the probability that all three of you win an autographed baseball?

The variance of a random variable X provides us with a measure of central location of the distribution of X.

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that exactly 10 foreclosure auctions occurred during a randomly selected five-day week in 2011 in Boston?

What are the two key properties of a discrete probability distribution?

Exhibit 5-5.The number of homes sold by a realtor during a month has the following probability distribution: Refer to Exhibit 5-5.What is the probability that the realtor sells no more than one house during a month?