Exam 7: Random Variables and Discrete Probability Distributions

The possible values of a Poisson random variable start at ____________________.

The number of days that a microcomputer goes without a breakdown is an example of a(n) ____________________ random variable.

NARRBEGIN: Number of Hamsters Number of Hamsters The joint probability distribution of X and Y is shown in the accompanying table, where X denotes the number of hamsters that Quinn may have next year, and Y denotes the number of hamsters that her boyfriend, Jason, may have when she moves in with him next year. X 1 1 0.4 0.1 2 0.3 0.2 NARREND -{Number of Hamsters Narrative} Determine the marginal probability distributions of X and Y.

NARRBEGIN: Katie's Portfolio Katie's Portfolio Katie is given the following information about the returns on two stocks: E(R₁) = 0.10, E(R₂) = 0.15, V(R₁) = 0.0225, and V(R₂) = 0.0441.NARREND -{Katie's Portfolio Narrative} Compute the expected value of the portfolio composed of 60% stock 1 and 40% stock 2.

Given that X is a discrete random variable, then the laws of expected value and variance can be applied to show that E(X + 5) = E(X) + 5, and V(X + 5) = V(X) + 25.

NARRBEGIN: Katie's Portfolio Katie's Portfolio Katie is given the following information about the returns on two stocks: E(R₁) = 0.10, E(R₂) = 0.15, V(R₁) = 0.0225, and V(R₂) = 0.0441.NARREND -{Katie's Portfolio Narrative} If Katie is most interested in maximizing her returns, which stock should she choose?

On the average, 1.6 customers per minute arrive at any one of the checkout counters of Sunshine food market. What type of probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in 10 minutes?

Which of the following is a discrete random variable?

If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between X and Y is a:

Let X be a Poisson random variable with $\mu$ = 6. Use the table of Poisson probabilities to calculate: a.P(X $\le$ 8) b.P(X = 8) c.P(X $\ge$ 5) d.P(6 $\le$ X $\le$ 10)

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 -{Online Bankers Narrative} Find the probability that at least 6 have profited from insider information.

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} Calculate E(X + Y) and V(X + Y) directly by using the probability distribution of X + Y.

If X is a binomial random variable with n = 25, and p = 0.25, then P(X = 25) = 1.0.

The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

If X and Y are random variables, the sum of all the conditional probabilities of X given a specific value of Y will always be:

Bivariate distributions provide probabilities of combinations of two variables.

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} Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation $\rho$ decreases.

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 4:00 and 5:00 P.M. is exactly two.

The binomial probability distribution is a discrete probability distribution.

A Poisson random variable is the number of successes that occur in a period of ____________________ or an interval of ____________________ in a Poisson experiment.