Chapter 6 - Statistical Distributions

Question 1

What is a Random Variable?

Answer 1

✯ A random variable is a variable represented by a capital letter (e.g. X,Y and Z etc.) that takes on the values that are the outcomes of an experiment.

Question 2

What are these scenarios modelled under?

Answer 2

✯ These scenarios are modelled under discrete uniform distribution.

Question 3

In what two ways can we represent the probability distribution of a random variable X?

Answer 3

1. Table Form

Or

2. Mass Function Form.

Question 4

What is a Discrete Random Variable?

Answer 4

✯ A discrete random variable takes on a finite number of values.

Question 5

What is a Continuous Random Variable?

Answer 5

✯ A continuous random variable takes on an infinite number of values.

Question 6

A discrete random variable X takes on a binomial distribution
X~B ( n, p) if what four conditions are met?

Answer 6

1. There is a fixed number of trials.
2. There is a fixed probability of success.
3. Trials are independent of one another.
4. There are only two possible outcomes: success of failure.

Question 7

What does the phrase ‘greater than 5 mean’?

How can this be calculated?

Answer 7

It means P (x > 5) = 1 - P( X ≤ 5)

Question 8

What does the phrase ‘no more than three’ mean?

How can this be calculated?

Answer 8

It means P (X ≤ 3)

Question 9

What does the phrase ‘at least 7’ mean?

Answer 9

It means P (X ≥ 7) = 1 - P(X ≤ 6)

Question 10

What does the phrase ‘fewer than 10’ mean?

Answer 10

It means P (X<10) = P(X≤ 9)

Question 11

What does the phrase ‘at most 8’ mean?

Answer 11

It means P (X ≤ 8)