Exam 7: Random Variables and Discrete Probability Distributions

Which of the following is a continuous random variable?

Retries The following table contains the probability distribution for X = the number of retries necessary to successfully transmit a 1024K data package through a double satellite media. -{Retries Narrative} What is the standard deviation of the number of retries?

Sports Fans Suppose that past history shows that 5% of college students are sports fans.A sample of 10 students is to be selected. -{Sports Fans Narrative} A sample of 100 students is to be selected.What is the average number that you would expect to sports fan?

If X and Y are independent, then COV(X, Y) = ____________________.

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. -{Mobile Phones Sales Narrative} Find the marginal probability distribution of the number of Blackberries sold daily.

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. -{Golfing Store Narrative} Find P(Y = 2 | X = 1)

The number of female customers out of a random sample of 100 customers arriving at a department store has a binomial distribution.

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. -{Elizabeth's Portfolio Narrative} Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are uncorrelated.

An auto insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance.A person's age is an example of a(n) ____________________ random variable.

Compute the following Poisson probabilities (to 4 decimal places) using the Poisson formula: a. P(X = 3), if $\mu$ = 2.5 b. P(X $\le$ 1), if $\mu$ = 2.0 c. P(X $\ge$ 2), if $\mu$ = 3.0

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. -{Number of Birds Narrative} Find the probability distribution of the random variable XY.

If X has a binomial distribution with n = 4 and p = 0.3, find P(X = 1).

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. -{Number of Birds Narrative} Calculate E(X + Y) directly by using the probability distribution of X + Y.

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit.Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour.Let X denote the number of vehicles that were exceeding the limit. -{Montana Highways Narrative} Find P(X = 10).

Sports Fans Suppose that past history shows that 5% of college students are sports fans.A sample of 10 students is to be selected. -{Sports Fans Narrative} Find the probability that less than 1 student is a sports fan.

In the notation below, X is the random variable, c is a constant, and V refers to the variance.Which of the following laws of variance is not true?

If n = 20 and p = 0.70, then the standard deviation of the binomial distribution is

The variance of X must be non-negative; the variance of Y must be non-negative; hence the covariance of X and Y must be non-negative.

The mean of a binomial distribution is equal to ____________________.

Car Sales The joint probability distribution of variables X and Y is shown in the table below.Rebecca and Rachel are car salespeople.Let X denote the number of cars that Rebecca will sell in a month, and let Y denote the number of cars Rachel will sell in a month. -{Car Sales Narrative} Calculate V(X) and V(Y).