Discrete Random Variables

What are the two primary characteristics of a probability density function (PDF) for a discrete random variable?

Which of the following scenarios is best modeled by a hypergeometric distribution?

A candy dish contains 30 jelly beans and 20 gumdrops. Ten candies are picked at random. What is the probability that exactly 5 of the 10 are gumdrops?

What are the three main characteristics of a binomial experiment?

According to Chapter 4, the binomial distribution can be used to approximate the hypergeometric distribution under what condition?

If you play a game 20 times, and your probability of winning any single game is 55 percent, what is the mean (mu) of the binomial distribution for the number of wins?

A key feature of the geometric distribution is that it is 'memoryless.' What does this mean in the context of an experiment?

A safety engineer examines accident reports until they find one caused by failure to follow instructions. If the probability of any given report showing this cause is 35 percent, what is the probability that the engineer must examine exactly 3 reports?

What are the two main characteristics of a Poisson experiment?

A bank expects to receive six bad checks per day on average. What is the probability of the bank getting fewer than five bad checks on any given day?

A call center receives an average of 147 emails per day. What is the standard deviation for this Poisson distribution?

When can the Poisson distribution be used to provide a good approximation for the binomial distribution?

In a survey of 500 seniors where 1 percent go on to get a Master's in Finance, what is the mean (mu) for the Poisson approximation of this binomial problem?

Which of the discrete probability distributions discussed in Chapter 4 is described as being 'memoryless'?

What is the key difference between a binomial experiment and a hypergeometric experiment?

A trainer is teaching a dolphin to catch a fish. The probability that the dolphin successfully catches a fish is 35 percent. Out of 20 attempts, what is the probability that the dolphin succeeds exactly 12 times?

For a geometric distribution where the random variable X is the number of failures BEFORE the first success, what is the formula for the mean (expected value)?

An office gets an average of 10 returns per day. The manager wants to know the probability of getting fewer than eight returns. This scenario is best modeled by which distribution?

The formula for the number of unique unordered subsets of size x that can be created from n unique elements is called the:

A bag has 44 vowels and 56 consonants. Seven tiles are picked at random. If you want to find the probability that four of the seven tiles are vowels, what is the group of interest and its size (A)?

Which of the following is NOT a characteristic of a Bernoulli Trial as defined in Chapter 4?

If a fair, six-sided die is rolled ten times, and we want to find the probability of rolling a 'one' more than three times, how should this probability question be stated mathematically?

A baseball player has a batting average of 0.320. What is the probability that he gets his first hit on his third trip to bat?

What is the expected number of trips to bat a hitter with a 0.320 batting average would need before getting a hit?

An emergency room gets an average of five patients per hour. A doctor wants to know the probability that the ER gets more than five patients per hour. Why is this a Poisson distribution problem?

If a random variable X has a Poisson distribution and is written as X ~ P(mu), what does the parameter 'mu' represent?

Leah receives about six telephone calls between 8 a.m. and 10 a.m. (a two-hour period). What is the value of mu for an interval of 15 minutes?

What is the relationship between the mean (mu) and the variance (sigma squared) in a Poisson distribution?

A study finds a probability of low seismic activity for the next 48 hours is 1.02 percent. What is the probability of low seismic activity in ten of the next 200 days, using the binomial distribution?

The Poisson distribution is often referred to as the 'waiting time' distribution. What does this name signify?

Which of the following is NOT a condition for a hypergeometric distribution to work?

In the binomial formula, what does the parameter 'q' represent?

A fair, six-sided die is rolled until a '3' appears. What is the probability that the first '3' appears on the fifth roll?

A city averages 12 traffic accidents per week. What is the probability of having exactly 10 accidents in a given week?

The random variable in a binomial distribution, X, is defined as what?

For a Poisson distribution, what does the random variable X represent?

If a manufacturing process has a 2 percent defect rate, what is the probability that the first defect is found on the seventh component tested?

What is the expected number of components you would need to test to find the first defect if the defect rate is 2 percent?

Approximately 70 percent of statistics students do their homework on time. In a class of 50 students, how would you define the random variable X if you are interested in the number of students who do their homework on time?

If 65 percent of people pass a driver's exam on the first try, and a group of 50 is selected, what is the standard deviation of X, the number of people who pass?

What is the random variable in a geometric experiment?

A key term in Chapter 4 is 'Probability Distribution Function (PDF)'. What does this function describe?

In a study of 420,019 cell phone users, 172 developed brain cancer. Which discrete distribution would be most appropriate to test the cancer rate?

The formula for the mean of a binomial distribution is mu = np. What is the formula for its variance?

A group of Martial Arts students includes 6 from Tae Kwon Do and 7 from Shotokan Karate. If 8 students are randomly picked, what are the possible values for X, the number of Shotokan Karate students picked?

In a binomial experiment, if the probability of success 'p' is 0.6, what is the probability of failure 'q'?

The number of times a person says 'uh' during a one-hour broadcast is an example of which type of random variable?

A standard deck of 52 cards is used. What is the probability of being dealt a 13-card hand that does not contain a heart?

A student takes a ten-question true-false quiz and randomly guesses each answer. What is the probability that the student passes with a grade of at least 70 percent?

The chance of an IRS audit for a tax return with over twenty-five thousand dollars in income is about 2 percent per year. What is the expected number of audits a person with that income has in a 20-year period?