Concept explainers
Grandparents Let X = the number of living grandparents that a randomly selected adult American has. According to recent General Social Surveys, its
- a. Does this refer to a discrete or a continuous random variable? Why?
- b. Show that the probabilities satisfy the two conditions for a probability distribution.
- c. Find the
mean of this probability distribution.
a.
Identify whether the random variable X is discrete or continuous.
Answer to Problem 52CP
The random variable X is discrete.
Explanation of Solution
The given information is that the random variable X is the number of living grandparents of a randomly selected American adult. From the survey, the probability distribution is approximately
Discrete random variable:
If the random variables, consider a set of distinct possible values for the trial then it is called discrete random variable.
Continuous random variable:
If the random variables, consider the possible values and it form an interval then it is called continuous random variable
In the given situation, the random variable X represents the number of grandparents and it will be a distinct number because the number of grandparents does not be in an interval.
Thus, the random variable X is discrete.
b.
Show that the probability values satisfy the probability distribution conditions.
Explanation of Solution
Conditions for the probability distribution:
- 1. For every value of x, the value of probability will lie between 0 and 1.
- 2. The total of all probabilities for the possible values of x is equal to 1.
From the given information, the all probability values lie between 0 and 1.
The sum of probabilities is,
Therefore, the total sum of probability distribution is 1.
Thus, the probability values satisfy the probability distribution conditions.
c.
Calculate the mean of the probability distribution.
Answer to Problem 52CP
The mean of the probability distribution is 0.50.
Explanation of Solution
Calculation:
The formula for mean is,
From the probability distribution, calculate the mean value for number of grandparents is,
Thus, the mean value is 0.50.
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Chapter 6 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
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