Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable that has a finite or countable number of possible outcomes.

Question 2

Suppose $$x is $$the number of defective light bulbs in a box of 100. Is $$x a $$discrete or continuous random variable? Why?

Accepted Answer

Discrete, because the number of defective bulbs can only be whole numbers.

Question 3

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

Accepted Answer

Each outcome must be equally likely.

Question 4

Given the following probability distribution for $$x$$: $$P(x=1)=0.2$$, $$P(x=2)=0.5$$, $$P(x=3)=0.3. Is $$this a valid probability distribution?

Accepted Answer

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

Question 5

A probability distribution is given as $$P(x=1)=0.4$$, $$P(x=2)=0.3$$, $$P(x=3)=0.4. Is $$this a probability distribution? Why or why not?

Accepted Answer

No, because the sum of the probabilities is greater than 1.

Question 6

How do you calculate the mean $$\mu of a $$discrete probability distribution?

Accepted Answer

$$\mu = \sum x \cdot P(x)$$

Question 7

Given the following probability distribution: $$x = 1, 2, 3$$ with $$P(x) = 0.2, 0.5, 0.3$$ respectively, what is the mean $$\mu$$?

Accepted Answer

$$\mu = 2.1$$

Question 8

Which formula correctly represents the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

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

Question 9

A company runs a raffle with 1000 tickets sold at $$1 each. There is one 500 $$prize and two $100 prizes. What is the expected value of buying one ticket?

Accepted Answer

$$E(x) = -0.30$$

Question 10

Which of the following statements about expected value is TRUE?

Accepted Answer

The expected value is the long-run average outcome of the random variable.

Question 11

Suppose a discrete probability distribution has $$\mu = 3$$ and $$\sigma = 1. $$According to the empirical rule, most data values will fall within which interval?

Accepted Answer

$$[2, 4]$$

Question 12

A probability distribution has $$P(x=1) = 0.2$$, $$P(x=2) = -0.1$$, $$P(x=3) = 0.9. Is $$this a valid probability distribution?

Accepted Answer

No, because one probability is negative.

Question 13

In the context of the personality inventory test for passive-aggressive traits, what does the mean score represent?

Accepted Answer

The long-run average score if the test were repeated many times.

Question 14

If a discrete probability distribution is symmetric, what can you say about its mean and median?

Accepted Answer

The mean and median are equal.

Question 15

A histogram of a discrete probability distribution has bars of width 1. What does the area of each bar represent?

Accepted Answer

The probability of the outcome.

Question 16

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

Accepted Answer

The number of students absent in a class on a given day.

Question 17

If the sum of the probabilities in a distribution is 0.95, what does this indicate?

Accepted Answer

The distribution is not valid because the probabilities must sum to 1.

Question 18

Which step is NOT part of constructing a discrete probability distribution from frequency data?

Accepted Answer

Multiply each frequency by the mean.

Discrete Probability Distributions: Study Notes

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