Statistics lesson 1

1. Lesson 1.1:
Random Variables and Probability
Distributions

2. Random Variables
- Is a set whose elements are the numbers assigned to the
outcomes of an experiment. It is usually denoted by uppercase
letters such as X, whose elements are denoted by a lower-case
letters, x1, x2, x3, and so on.
- For instance, if a coin is tossed twice, the set of all possible
outcomes (S) of the experiment is:
S = {HH, HT, TH, TT}

3. If we are interested in the number of tails that came out in the
experiment, then we can assign numbers 0, 1 and 2 for each of
the 4 possible outcomes. Thus, we can write
Sample
Space
Number of
Tails
HH 0
HT 1
TH 1
TT 2
From the table above, instead of
writing number of tails, we can
denote it as X = {0,1,2}
Then X is called Random Variables

4. Types of Random Variables
1. Discrete random variables
- A random variable X is said to discrete random variable if it has a
finite number of elements or infinite but can be represented by whole
numbers. These values usually arise from counts.
2. Continuous random variable
- A random variable Y is said to be continuous random variable if it has
infinite number of elements and cannot be represented by whole
numbers. These values usually arise from measurements

5. Example 1: A teacher’s record has the following
X = Scores of students in a 50-item test
Y = Gender of selected students
Z = Height of randomly selected grade 11 students
Classify each variable above as Discrete or Continuous
Solutions:
X is a discrete random variable
Y is a discrete random variable
Z is a continuous random variables

6. 1. X is a discrete random variable because the scores of
the students are represented by whole number
2. Y is a discrete random variable because male and female
could be counted
3. Z is a continuous random variables because between
two values of height, there are always infinite numbers of
possible values for height. The values of height can be
measurable

7. Example 2: Write the possible values of each random variable:
a. X = number of tail in tossing a coin thrice
b. Y = drop-out rate (%) in a certain high school
c. Z = number of even number outcomes in a roll of a die
Solution:
a. X = {0, 1, 2, 3}
b. Y = {0 ≤ 𝑥 ≤ 100}
c. Z = {2, 4, 6}

8. Example 3: Write the possible values of each random variables
1. X = number of heads in tossing a coin three times
2. Y = failure rate (%) in a certain high school
3. Z = number of female among 6 nurses
4. X = number of odd number outcomes in a roll of a dice
5. Y = weight (in mg) of a powder that does not exceed 80 mg
6. D = product of two numbers taken from a boxes containing
number 0 through 5
7. A = length (in cm) of a shoelace that is not longer 2 meters
8. B = scores of a students in a 500-item test