Question 1

Which of the following best describes a random variable?

Accepted Answer

A numerical measurement of the outcome of a random phenomenon.

Question 2

Suppose you flip a coin three times. Let $$X be $$the number of heads observed. Which of the following is a possible value for $$X$$?

Accepted Answer

2

Question 3

What is the defining property of a probability distribution for a discrete random variable $$X$$?

Accepted Answer

The sum of the probabilities for all possible values of $$X$$ equals 1.

Question 4

In a best of seven series, what is the probability that the series will be decided by at least six games?

Accepted Answer

$$0.625$$

Question 5

Which formula correctly represents the mean (expected value) of a discrete probability distribution?

Accepted Answer

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

Question 6

If a random variable $$X$$ can take values 0 and 1, and the probability of $$X=1 is$$ $$0.3$$, what is the mean of $$X$$?

Accepted Answer

$$0.3$$

Question 7

You are given $$1000 to invest. You can choose a sure gain of 500$$, or a 0.5 chance to gain $1000 and a 0.5 chance to gain nothing. What is the expected gain for the risk-taking strategy?

Accepted Answer

$$500$$

Question 8

Which of the following statements about the standard deviation $$\sigma of a $$probability distribution is correct?

Accepted Answer

$$\sigma$$ measures the variability from the mean.

Question 9

For a continuous random variable, how is the probability that the variable falls within a particular interval determined?

Accepted Answer

By the area under the probability distribution curve above the interval.

Question 10

Which of the following is NOT a property of a probability distribution for a continuous random variable?

Accepted Answer

The probability for a single exact value is always greater than zero.

Question 11

A random variable is called continuous when:

Accepted Answer

Its possible values form an interval.

Question 12

If $$X is a $$discrete random variable with possible values $$x_1$$, $$x_2$$, ..., x_n$$ and probabilities P$$($$x_1$$), P($$x_2$$), ..., P(x_n)$$, which of the following must be true?

Accepted Answer

$$\sum_{i=1}^{n} P(x_i) = 1$$

Question 13

In the context of probability distributions, what is a parameter?

Accepted Answer

A numerical summary of a population or probability distribution, often denoted by Greek letters.

Question 14

Which of the following best describes the expected value of a random variable?

Accepted Answer

The average value expected in a long run of observations.

Question 15

A probability distribution for a categorical variable with two categories is often coded as 0 and 1. What does the mean of this distribution represent?

Accepted Answer

The probability of the outcome coded as 1.

(Lecture 13) Probability Distributions: Discrete and Continuous Random Variables

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