UNIT 6

Question 1

Discrete Random Variable

Answer 1

A discrete random variable takes a fixed set of possible values with gaps between.

Question 2

Continuous Random Variable

Answer 2

A continuous random variable takes on any value in an interval of values so there are infinitely many values. The probability distribution is described by a density curve.

The probability of each individual
outcome is 0. Only an interval of values will have a numerical (other than 0) probability.

Question 3

Interpreting the Expected Value

mean

Answer 3

The mean/expected value of a random variable is the long-run average outcome of a random phenomenon carried out a very large number of
times.

Question 4

Conditions of a Binomial

Distribution

Answer 4

1. Binary? Trials can be classified as success/failure
2. Independent? Trials must be independent.
3. Number? The number of trials must be determined in advance.
4. Success? The probability of success (p) must be the

Question 5

Conditions of a Geometric

Distribution

Answer 5

1. Binary? Trials can be classified as success/failure
2. Independent? Trials must be independent.
3. Trials? The goal is to count the number of trials until the first success occurs.
4. Success? The probability of success (p) must be the same for each trial.

Question 6

Binomial Distribution

Calculator Usage

Answer 6

Exactly 5: P(X = 5) →Binomialpdf(n,p,5)

At most 5: P(X ≤ 5) →Binomialcdf(n,p,5)

Less than 5: P(X <5) →Binomialcdf(n,p,4)

At least 5: P(X ≥5) →1 - Binomialcdf(n,p,4)

More than 5: P(X >5) →1 - Binomialcdf(n,p,5)

Question 7

10% rule

Answer 7

When taking an SRS of size n from a population of size N, we can sample without replacement (violating the independence condition) as long as we sample less than 10% of the population.