30 Questions
Which type of random variable has a continuum of possible values?
Continuous random variable
What is the number of possible values for a discrete random variable?
Countable
Which of the following is an example of a continuous random variable?
Temperature of a solution
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}
Which of the following is an example of a discrete random variable?
Number of coins in a jar
What is the number of possible outcomes for the gender random variable?
2
What is the random variable of interest in the example provided?
Number of defective units
What are the possible discrete values for the number of defectives among the sample?
0, 1, 2, 3, 4
What is the probability of having 0 defectives among the sample?
0.6561
How is the probability of having 1 defective unit calculated?
$0.93 \times 0.1$
What does the counting rule for combinations help in counting?
Possible ways binomial events can occur
What is the sample size used in the example provided?
$\frac{4}{300}$ relative to population size
What happens to the skewness of the binomial distribution when n is small and p approaches 0 or 1?
It becomes more pronounced
When does the binomial distribution become more bell-shaped?
When n increases
What characteristic defines situations where the Poisson distribution is used instead of the binomial distribution?
The outcomes are rare relative to the possible outcomes
What is the average number of outcomes of interest per unit time or space interval in a Poisson Distribution?
$rac{ ext{total outcomes}}{ ext{unit time}}$
In a Poisson Distribution, how are the number of outcomes of interest treated?
As random
What does the Poisson Distribution Formula represent?
Probability that an outcome of interest occurs in a given segment
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.
What is considered a 'success' in the context of the binomial distribution for Household Security?
Discovering a unit with a manufacturing defect.
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.
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.
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%
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.
What does 𝜇 represent in the context of the Poisson Distribution formula?
Mean number of occurrences in an interval
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
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
In the Poisson Distribution formula, what does x represent?
Number of successes in a segment of interest
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
What happens to the Poisson probability as the number of arrivals increases above the mean number of occurrences?
Decreases
This quiz covers the types of random variables discussed in UGBS 202: discrete and continuous. It includes definitions and examples of discrete random variables with a finite number of values, and continuous random variables with a continuum of values.
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