Exam 6: Random Variables and Discrete Probability Distributions

A random variable is a function or rule that assigns a number to each outcome of an experiment.

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

Which of the following is not a required condition for the distribution of a discrete random variable X that can assume values x_i ?

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. {Unsafe Levels of Radioactivity Narrative} Find the probability that there will be no more than 1 incident in a year.

For a random variable X , V ( X + 3)= V ( X + 6), where V refers to the variance.

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. {Stress Narrative} Find the probability distribution of X .

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. {Post Office Narrative} Find the probability that the number of arrivals between 3:00 and 5:00 P.M. is at least 10.

In the Poisson distribution, the mean is equal to the ____________________.

Compute the following Poisson probabilities (to 4 decimal places)using the Poisson formula:

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. {Stress Narrative} Find P ( X

The standard deviation of a binomial random variable X is given by the formula s ² = np (1 - p ), where n is the number of trials, and p is the probability of success.

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.

The time required to drive from New York to New Mexico is a discrete random variable.

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} Apply the laws of expected value to find the following: a. E ( X ²) b. E (2 X ² + 5) c. E ( X - 2)²

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

A community college has 150 word processors. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 25 of the word processors will require repair, one will use what type of probability distribution?

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

The dean of students conducted a survey on campus. Grade point average (GPA)is an example of a(n)____________________ random variable.

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

Gym Visits Let X represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: {Gym Visits Narrative} What is the probability that the student visits the gym at most twice in a month?