Exam 7: Random Variables and Discrete Probability Distributions

The number of customers making a purchase out of 30 randomly selected customers has a Poisson distribution.

NARRBEGIN: 911 Phone Calls 911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center.NARREND -{911 Phone Calls Narrative} If no calls are currently being processed, what is the probability that the desk employee can take four minutes break without being interrupted?

The ____________________ and the ____________________ both measure the relationship between two random variables X and Y.

NARRBEGIN: Online Bankers Online Bankers An official from the securities commission estimates that 75% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry.NARREND -A remedial program evenly enrolls tradition and non-traditional students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new on-line class, what is the probability that all 4 students selected are traditional students?

The binomial distribution deals with consecutive trials, each of which has two possible outcomes.

In a Poisson experiment, the probability of a success in an interval is ____________________ to the size of the interval.

NARRBEGIN: Online Bankers Online Bankers An official from the securities commission estimates that 75% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry.NARREND -Let X be a binomial random variable with n = 25 and p = 0.01. a.Use the binomial table to find P(X = 0), P(X = 1), and P(X = 2). b.Find the variance and standard deviation of X.

NARRBEGIN: Post office Post office The number of arrivals at a local post office between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12.NARREND -{Post Office Narrative} Find the probability that the number of arrivals between 3:30 and 4:00 P.M. is at least 10.

The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is:

If X and Y are two variables with E(XY) = 10.56, E(X) = 4.22, and E(Y) = 5.34, then COV(X, Y) = 1.0.

NARRBEGIN: Shopping Outlet Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. 0 1 2 3 4 ( ) 0.05 0.35 0.25 \square.20 0.15 NARREND -{Shopping Outlet Narrative} Find the expected value of the number of stores entered.

In a Poisson experiment, the number of successes that occur in any interval of time is ____________________ of the number of success that occur in any other interval.

NARRBEGIN: Number of Horses Number of Horses The random variable X represents the number of horses per family in a rural area in Iowa, with the probability distribution: p(x) = 0.05x, x = 2, 3, 4, 5, or 6.NARREND -{Number of Horses Narrative} Express the probability distribution in tabular form.

NARRBEGIN: Number of Birds Number of Birds Alana and Eva are sisters. Let X denote the number of birds that Alana may have in the next two years, and let Y denote the number of birds Eva may have during the same period. The marginal probability distributions of X and Y are shown below. 0 1 2 ( ) 0.5 0.3 0.2 y 0 1 2 ( ) 0.4 0.5 0.1 NARREND -{Number of Birds Narrative} Assume that X and Y are independent and find their bivariate distribution.

NARRBEGIN: Golfing Store Golfing Store The joint probability distribution of variables X and Y is shown in the table below, where X is the number of drivers and Y is the number of putters sold daily in a small golfing store. X 1 2 3 1 0.30 0.18 0.12 2 0.15 0.09 0.06 3 0.05 0.03 0.02 NARREND -{Golfing Store Narrative} Are X and Y independent? Explain.

NARRBEGIN: Unsafe Levels of Radioact Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND -{Unsafe Levels of Radioactiviy Narrative} Find the probability that there will be at least 1 incident in a year.

NARRBEGIN: Mobile Phones Sales Mobile Phones Sales After analyzing sales data, the owner of a Mobile Phone store produced the following joint probability distribution of the number of iPhones (X) and Blackberries (Y) sold daily. X 1 1 0.4 0.1 2 0.3 0.2 NARREND -{Mobile Phones Sales Narrative} Compute the variance of the number of Blackberries sold daily.

NARRBEGIN: Elizabeth's Portfolio Elizabeth's Portfolio Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively.NARREND -{Elizabeth's Portfolio Narrative} Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are perfectly positively correlated.

The amount of time that a microcomputer is used per week is an example of a(n) ____________________ random variable.

NARRBEGIN: Unsafe Levels of Radioact Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND -{Unsafe Levels of Radioactivity Narrative} Find the variance of the number of incidents in one year.