Exam 6: Random Variables and Discrete Probability Distributions

Which of the following is a discrete random variable?

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

Faculty rank (professor, associate professor, assistant professor, and lecturer) is an example of a discrete random variable.

Suppose that the number of buses arriving at a Depot per minute is a Poisson process. If the average number of buses arriving per minute is 3, what is the probability that exactly 6 buses arrive in the next minute?

If X has a binomial distribution with n = 4 and p = 0.3, find the probability that X is at most one.

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

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.

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. -Find P(X = 2).

Stress: Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed. -Find the probability distribution of X.

A function or rule that assigns a numerical value to each simple event of an experiment is called:

Which of the following cannot have a Poisson distribution?

If X has a binomial distribution with n = 4 and p = 0.3, find the probability that X is at least one.

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.

The binomial random variable is the number of successes that occur in a fixed period of time.

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. -Find the standard deviation of the number of incidents is in one year.

In a(n) ____________________ experiment, the probability of a success in an interval is the same for all equal-sized intervals.

In a Poisson distribution, the variance and standard deviation are equal.

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. -What is the variance for the number of retries?

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. -Find the expected number of vehicles that are traveling on Montana highways and exceeding the speed limit.

What is the probability that the student visits the gym at most twice in a month?