Exam 5: Some Important Discrete Probability Distributions

A campus program evenly enrols undergraduate and graduate students.If a random sample of four students is selected from the program to be interviewed about the introduction of a new fast-food outlet on the ground floor of the campus building,what is the probability that all four students selected are undergraduate students?

Which of the following statements about the covariance between two discrete random variables is true?

Instruction 5.4 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently. -Referring to Instruction 5.4,the probability that at least one sounds an alarm in the presence of smoke is ______

Instruction 5.3 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the total standard deviation of value gain if you invest in both houses?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be no more than 1 power outage in a year is______

Instruction 5.7 A major airline keeps a record of the number of mishandled bags per 1,000 customers. In 2011, the airline had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5.7,what is the probability that in the next 1,000 customers,the airline will have no more than two and at least eight mishandled bags?

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. -Find the probability that more than three bankruptcies occur next month.

The local police department must write,on average,five tickets a day to keep department revenues at budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. -Find the probability that less than six tickets are written on a randomly selected day from this population.

Instruction 5.7 A major airline keeps a record of the number of mishandled bags per 1,000 customers. In 2011, the airline had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5.7,what is the probability that in the next 1,000 customers,the airline will have no more than four mishandled bags?

If p remains constant in a binomial distribution,an increase in n will not change the mean.

A financial analyst is presented with information on the past records of 60 start-up companies and told that in fact only three of them have managed to become highly successful.He selected three companies from this group as the candidates for success.To analyse his ability to identify the companies that will eventually become highly successful,he will use what type of probability distribution?

The portfolio expected return of two investments

The probability that a particular brand of smoke alarm will malfunction in the presence of smoke is 0.002.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at most 5,000 of them will malfunction in case of a fire?

Instruction 5.7 A major airline keeps a record of the number of mishandled bags per 1,000 customers. In 2011, the airline had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5.7,what is the probability that in the next 1,000 customers,the airline will have more than ten mishandled bags?

A probability distribution for a discrete random variable is a mutually exclusive list of all possible numerical outcomes of the random variable with the probability of occurrence associated with each outcome.

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of 2 or more 000 calls in a day is ______

In a Poisson distribution,the mean and variance are equal.

Numerical variables are classified as either discrete or continuous.

A continuous variable has an outcome that arises from a counting process rather than a measuring process.

The largest value that a Poisson random variable X can have is n.