Prelims

Question 1

What is a population parameter?

Answer 1

A summary measure describing a characteristic of the population using population data.

Question 2

What is a sample statistic?

Answer 2

A summary measure describing a characteristic of the sample using sample data.

Question 3

What is the difference between a parameter and a statistic?

Answer 3

Parameter uses population data, statistic uses sample data.

Question 4

What is a random experiment?

Answer 4

A process repeatable under similar conditions but with unpredictable outcomes.

Question 5

What is a sample space?

Answer 5

The set of all possible outcomes of a random experiment.

Question 6

What is an event?

Answer 6

A subset of the sample space.

Question 7

What is the symbol for a sample space?

Answer 7

Ω

Question 8

What are the two methods to specify a set?

Answer 8

Roster method and rule method.

Question 9

What is SRSWOR?

Answer 9

Simple random sampling without replacement.

Question 10

What is SRSWR?

Answer 10

Simple random sampling with replacement.

Question 11

What is the probability of the sample space (sure event)?

Answer 11

1

Question 12

What is the probability of the empty set (impossible event)?

Answer 12

0

Question 13

What is the formula for classical probability?

Answer 13

P(A) = n(A) / n(Ω)

Question 14

What does ‘mutually exclusive’ mean?

Answer 14

Events cannot happen at the same time.

Question 15

What is the formula for the union of two events?

Answer 15

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Question 16

What is the formula for the complement of an event?

Answer 16

P(Aᶜ) = 1 - P(A)

Question 17

When are events independent?

Answer 17

If P(A ∩ B) = P(A) * P(B)

Question 18

What are the three approaches to assigning probability?

Answer 18

Classical, relative frequency, and subjective.

Question 19

What is a random variable?

Answer 19

A function that assigns a real number to each outcome in the sample space.

Question 20

What is the range of probability values?

Answer 20

From 0 to 1

Question 21

What is a discrete random variable?

Answer 21

A variable that can take a countable number of values.

Question 22

What is an example of a discrete random variable?

Answer 22

Number of heads in 3 coin tosses.

Question 23

What is a probability mass function (PMF)?

Answer 23

A function that gives the probability that a discrete random variable is exactly equal to some value.

Question 24

What is the total of all probabilities in a PMF?

Answer 24

1

Question 25

What is the binomial distribution used for?

Answer 25

To model the number of successes in a fixed number of independent trials.

Question 26

What is the formula for a binomial probability?

Answer 26

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Question 27

What are the conditions for a binomial experiment?

Answer 27

Fixed number of trials, independent, two outcomes, constant probability.

Question 28

What is the normal distribution?

Answer 28

A continuous probability distribution that is symmetric and bell-shaped.

Question 29

What are the key parameters of a normal distribution?

Answer 29

Mean (μ) and standard deviation (σ).

Question 30

What does the empirical rule state?

Answer 30

68%-95%-99.7% of data falls within 1, 2, 3 standard deviations from the mean.