UGBS 202: Types of Random Variables Review

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Which type of random variable has a continuum of possible values?

Nominal random variable

Discrete random variable

Dichotomous random variable

Continuous random variable (correct)

What is the number of possible values for a discrete random variable?

Countable (correct)

Fixed

Uncountable

Infinite

Which of the following is an example of a continuous random variable?

Number of cars in a parking lot

Number of pens on a desk

Temperature of a solution (correct)

Number of students in a class

If a die is rolled twice, what are the possible values for the random variable representing the number of times a 4 comes up?

{0, 1, 2} Signup and view all the answers

Which of the following is an example of a discrete random variable?

Number of coins in a jar Signup and view all the answers

What is the number of possible outcomes for the gender random variable?

2 Signup and view all the answers

What is the random variable of interest in the example provided?

Number of defective units Signup and view all the answers

What are the possible discrete values for the number of defectives among the sample?

0, 1, 2, 3, 4 Signup and view all the answers

What is the probability of having 0 defectives among the sample?

0.6561 Signup and view all the answers

How is the probability of having 1 defective unit calculated?

$0.93 \times 0.1$ Signup and view all the answers

What does the counting rule for combinations help in counting?

Possible ways binomial events can occur Signup and view all the answers

What is the sample size used in the example provided?

$\frac{4}{300}$ relative to population size Signup and view all the answers

What happens to the skewness of the binomial distribution when n is small and p approaches 0 or 1?

It becomes more pronounced Signup and view all the answers

When does the binomial distribution become more bell-shaped?

When n increases Signup and view all the answers

What characteristic defines situations where the Poisson distribution is used instead of the binomial distribution?

The outcomes are rare relative to the possible outcomes Signup and view all the answers

What is the average number of outcomes of interest per unit time or space interval in a Poisson Distribution?

$rac{ ext{total outcomes}}{ ext{unit time}}$ Signup and view all the answers

In a Poisson Distribution, how are the number of outcomes of interest treated?

As random Signup and view all the answers

What does the Poisson Distribution Formula represent?

Probability that an outcome of interest occurs in a given segment Signup and view all the answers

What is a condition for the binomial distribution to apply to the situation described in the text?

There must be only two possible outcomes when a unit is installed. Signup and view all the answers

What is considered a 'success' in the context of the binomial distribution for Household Security?

Discovering a unit with a manufacturing defect. Signup and view all the answers

Why is it crucial for each security unit to be designed and made in the same way for the binomial distribution to apply?

To meet standard quality requirements. Signup and view all the answers

What happens if a unit has either a design or production problem according to the text?

It will require more than one day to install. Signup and view all the answers

What percentage of security units at Household Security are expected to have problems requiring more than one day to install when operating at standard quality?

10% Signup and view all the answers

Why does the probability of a defective unit need to remain constant from unit to unit for the binomial distribution to be applicable?

To satisfy a condition for independent trials. Signup and view all the answers

What does 𝜇 represent in the context of the Poisson Distribution formula?

Mean number of occurrences in an interval Signup and view all the answers

If the average number of arrivals at Whole Foods per hour is 16, what is the expected number of arrivals in a 2-hour segment?

16 Signup and view all the answers

What is the probability of 15 arrivals at Mercy Hospital's emergency room in an hour if the average rate is 6 per hour?

0.0012 Signup and view all the answers

In the Poisson Distribution formula, what does x represent?

Number of successes in a segment of interest Signup and view all the answers

If the average arrival rate at Whole Foods is 10 per hour, what is the probability of exactly 8 arrivals in 45 minutes?

0.0567 Signup and view all the answers

What happens to the Poisson probability as the number of arrivals increases above the mean number of occurrences?

Decreases Signup and view all the answers