Question 1

For the probability distribution of a discrete random variable, which formula can be used to compute the mean (expected value) $$\mu$$?

Accepted Answer

$$\mu = \sum x_i P(x_i)$$

Question 2

Which of the following is NOT a requirement for a discrete probability distribution?

Accepted Answer

Each outcome must be equally likely.

Question 3

A random variable is said to be continuous if:

Accepted Answer

It can take on any value within an interval.

Question 4

Given the following probability distribution, determine if it is a valid discrete probability distribution:

$$\begin{array}{c|cccc}
x & 1 & 2 & 3 & 4 \
\hline
P(x) & 0.2 & 0.3 & 0.4 & 0.1 \
\end{array}$$

Accepted Answer

Yes, because all probabilities are between 0 and 1 and sum to 1.

Question 5

Suppose the probability distribution for the number of children killed in school shootings is given as follows:

$$\begin{array}{c|cccc}
	ext{Children Killed} & 0 & 1 & 2 & 3 \
\hline
P(x) & 0.60 & 0.20 & 0.08 & 0.07 \
\end{array}$$

What is the probability that at least one child was killed?

Accepted Answer

$$0.40$$

Question 6

Given the following probability distribution:

$$\begin{array}{c|cccc}
x & 0 & 1 & 2 & 3 \
\hline
P(x) & 0.1 & 0.3 & 0.4 & 0.2 \
\end{array}$$

Compute the mean $$\mu of $$the distribution.

Accepted Answer

$$1.7$$

Question 7

A survey of high school students found the following probability distribution for the age (in years) at which they first had sex:

$$\begin{array}{c|cccccc}
	ext{Age} & 11 & 12 & 13 & 14 & 15 & 16 \
\hline
P(x) & 0.01 & 0.07 & 0.06 & 0.15 & 0.21 & 0.26 \
\end{array}$$

What is the interpretation of the mean of this distribution?

Accepted Answer

It is the average age at which high school students first had sex.

Question 8

If a probability distribution is skewed right, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 9

Suppose a life insurance company sells a $$\100$$,000$$ one-year term life insurance policy to a 21-year-old female for $$\$$250. $$The probability that the female survives the year is $$0.99958. $$What is the expected value of this policy to the insurance company?

Accepted Answer

$$\171.45$

Question 10

A cancer patient coaching organization offers three programs with the following total charges (in dollars) and probabilities:

$$\begin{array}{c|ccc}
	ext{Program} & 	ext{Total Charge} & P(x) \
A & 768 & 0.376 \
B & 1060 & 0.600 \
C & 1690 & 0.024 \
\end{array}$$

What is the expected total charge per client?

Accepted Answer

$$1042.16$$

Question 11

Which of the following statements about the median of a probability distribution is TRUE?

Accepted Answer

The median is resistant to extreme values.

Question 12

Suppose the probability distribution for the number of sex partners among a group of students is as follows:

$$\begin{array}{c|cccccc}
	ext{Partners} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline
P(x) & 0.50 & 0.17 & 0.14 & 0.07 & 0.06 & 0.06 \
\end{array}$$

What is the probability that a randomly selected student had fewer than 2 sex partners?

Accepted Answer

$$0.67$$

Question 13

Given a discrete probability distribution, which of the following is the correct formula for the variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \sum (x_i - \mu)^2$ P(x_i)$$

Question 14

A probability distribution is given by:

$$\begin{array}{c|cccc}
x & 1 & 2 & 3 & 4 \
\hline
P(x) & 0.1 & 0.2 & 0.3 & 0.4 \
\end{array}$$

What is the standard deviation $$\sigma of $$this distribution? (Round to two decimal places.)

Accepted Answer

$$1.12$$

Question 15

Which of the following best describes the shape of a probability distribution where the mean is less than the median?

Accepted Answer

Skewed left

Question 16

If a probability distribution is symmetric, which of the following is true?

Accepted Answer

The mean and median are equal.

Question 17

A table shows the number of bald eagles in a country over time. Is the random variable representing the number of bald eagles discrete or continuous?

Accepted Answer

Discrete, because the number of eagles can only take integer values.

Question 18

Suppose a probability distribution is given for the number of heads in three coin tosses. Which of the following is a possible value for the mean?

Accepted Answer

1.5

Question 19

Which of the following is a real-world example of a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour.

Discrete Probability Distributions and Expected Value: Study Notes

스터디 가이드 - 연습 문제

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