Exam 7: Random Variables and Discrete Probability Distributions

Number of Motorcycles The probability distribution of a discrete random variable X is shown below, where X represents the number of motorcycles owned by a family. -{Number of Motorcycles Narrative} Find the following probabilities: a. P(X > 1) b. P(X $\le$ 2) c. P(1 $\le$ X $\le$ 2) d. P(0 < X < 1) e. P(1 $\le$ X < 3)

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?

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(4 < X < 9).

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.How long a person has been a licensed rider is an example of a(n) ____________________ random variable.

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. -{Number of Horses Narrative} Find the expected number of horses per family.

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 + 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 = 2).

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?

The sum of the expected values always equals the expected value of the sums.

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

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:

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 standard deviation of the number of sports fans you expect?

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(3 $\le$ X $\le$ 6).

A portfolio return, R_p, of two stocks with individual returns, R₁ and R₂, is, in general, given by R_p = R₁ + R₂.

In a bivariate distribution, the sum of all the ____________________ probabilities must equal 1.

The variance of a binomial distribution is equal to ____________________.

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} Compute the mean and variance of Y.

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

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. -{Number of Hamsters Narrative} Calculate all possible values of the conditional probabilities, for X given Y and for Y given X.

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. -{Number of Hamsters Narrative} Calculate E(XY).