Lectures 7 & 8 Conceptual Short-Answer

Question 1

Explain what a random experiment is.

Answer 1

A random experiment is a well-defined procedure or action that randomly produces an observable outcome in the sample space.

Question 2

What is a sample space?

Answer 2

The set of all possible outcomes from a random experiment

Question 3

What is an outcome?

Answer 3

Result of a random experiment

Question 4

What does it mean for an experiment to be random?

Answer 4

Actual outcome cannot be determined in advance

Question 5

Describe 2 properties of outcomes in a sample space must satisfy.

Answer 5

Must be exhaustive and mutually exclusive

Question 6

What does it mean for outcomes in a sample space to be “exhaustive”?

Answer 6

All possible outcomes must be listed in the sample space, each trial (or experiment) must result in one of these outcomes in the sample space

Question 7

What does it mean for outcomes in a sample space to be “mutually exclusive”?

Answer 7

No 2 outcomes can occur at the same time (on the same “trial”)

Question 8

What is an event of a random experiment?

Answer 8

A subset of the sample space or a set of outcomes in the sample space

Question 9

What is the probability?

Answer 9

A mathematical function of an event in a sample space, quantifying the likelihood of that event occurring in accordance with specific axiomatic rules

Question 10

What does “0≤𝑃(𝐸)≤1” mean?

Answer 10

Probability that any event must lie between 0 and 1, inclusive

Question 11

What does “P(E) = 1” mean?

Answer 11

Probability than an event (E) is certain to occur

Question 12

What does “𝑃(𝑆) = 1” mean?

Answer 12

Probability that any of the outcomes in S occurs must be 1

Question 13

Let A and B denote events of a random experiment. Then, what does the statement “P(A|B) =/= P(B|A)” mean?

Answer 13

The conditional probability of event A given B is generally not the same as the probability of event B given A

Question 14

How does a classical approach assign probabilities to events?

Answer 14

Assigns based on logic, by assuming outcomes are equally likely
P(E) = (Number of possibles outcomes in which E occurs) / (Total number of possible outcomes)

Question 15

How does a relative frequency approach assign probabilities to events?

Answer 15

Assigns probabilities on the basis of data
P(E) = (Number of trials in which E occurs) / (Total number of trials)

Question 16

How does a subjective approach assign probabilities to events?

Answer 16

Assigns probabilities on the basis of personal belief or prior experiences
P(E) = Your best guess

Question 17

What does 𝑃(𝑋 = 𝑥𝑖) ≥ 0 𝑖𝑓 𝑥𝑖 ∈ 𝑆 mean?

Answer 17

The probability of any outcome xi for the random variable X must be non-negative

Question 18

What does ∑ 𝑃(𝑋 = 𝑥𝑖)∞
𝑖=1 = 1 𝑖𝑓 𝑥𝑖 ∈ 𝑆 mean?

Answer 18

The sum of the probabilities for all possible outcomes of X must equal 1

Question 19

What does 𝑃(𝑋 = 𝑥) = 0 𝑓𝑜𝑟 𝑥 ∉ 𝑆 mean?

Answer 19

The probability of any outcome X that is not in the sample space S is zero, meaning events outside the sample space cannot occur