Exam 4: Discrete Random Variables and Probability Distributions

A random variable which takes on no more than a countable number of values is called a(n):

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table displays the joint probability distribution of two discrete random variables X and Y. -Determine the marginal probability distribution for X.

Portfolio analysis and construction is conducted using probability distributions.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,there are 3.2 defects in a sheet of rolled steel.Assume that the number of defects follows a Poisson distribution. -What is the probability of having more than three defects in a roll?

The probability distribution contains all the information about the probability properties of a random variable.

Calculate the correlation between weekly take-home pay and amount spent weekly on recreational activities.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table displays the joint probability distribution of two discrete random variables X and Y. -Compute the correlation between X and Y.

The expected value of a discrete random variable can be shown to be the weighted average over all possible outcomes.

Find the probability distribution of the random variable X + Y.

Which of the following can be used to approximate the binomial distribution when the number of trials n is large and the probability of success P is small such that nP ≤ 7?

The binomial distribution is widely used in business applications.Why do you think this is the case?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: In a recent survey of 300 teenagers,62% of the teenagers indicated that they had been to a movie within the past month.75% of those teenagers who had seen a movie also had gone out to dinner in the past month,while only 64% of the teenagers who had not seen a movie had been out to dinner in the past month.Define the random variables as follows: X = 1 if teenager had been to movie;X = 0 otherwise Y = 1 if teenager had been out to dinner;Y = 0 otherwise -Find the conditional probability function of X,given Y = 1.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees. -What is the probability that at least two of the trainees will still be employed at the end of nine months?

The following table lists the relative frequency distribution of the number of calls coming into a call center each hour.If each call takes five minutes to process,what is the mean and standard deviation of the number of minutes the operators are answering questions each hour?

The sum of the product of each value of a discrete random variable X and its probability is referred to as its:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution. -It has been estimated that 30% of all farms are family-owned.In a sample of 12 farms,what is the probability that exactly three farms are family owned?

A cooler contains 14 drinks: 8 soft drinks and 6 beers.You select 3 drinks from the cooler.Let the random variable X be the number of soft drinks you get out of 3.Develop the probability distribution function of X.

In general,the variance of the sum of two random variables is the sum of their variances.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. -What is the standard deviation of the number of pieces of junk mail you receive daily?

The probability distribution function can be represented in a graph once the probabilities have been: