This presentation the statistics teachers to discuss discrete random variable since it includes examples and solutions.
Content:
-definition of random variable
-creating a frequency distribution table
- creating a histogram
-solving for the mean, variance and standard deviation.
References:
http://www.elcamino.edu/faculty/klaureano/documents/math%20150/chapternotes/chapter6.sullivan.pdf
https://www.mathsisfun.com/data/random-variables-mean-variance.html
https://www.youtube.com/watch?v=OvTEhNL96v0
https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214891-eng.htm
2. Definitions
Random Variable – a variable whose
variables are determined by
chance.
Discrete Probability Distribution –
Consist of random variables and
probabilities of the values.
3. Requirements of a Probability
Distribution
1. All probabilities must between 0 and 1.
2. The sum of probabilities must add up to 1.
4. Example: Basic Concept of Probability
Review:
What is the probability of having two tails
in flipping a coin twice?
What is the probability of getting the
numbers 1 and 5 in rolling a die.
5. Example: Basic Concept of Probability
Review:
In a group of 40 people, 15 have high blood
pressure and 25 have high level of cholesterol,
what is the probability that a person that will be
randomly selected have
a) has high blood pressure (event A)?
b) has high level of cholesterol(event B)?
6. Example: Probability Distribution of
Random Variable
1. Construct a probability distribution
for drawing a card from a deck of
40cards consisting of 10 cards
numbered 1, 10 cards numbered
2, 15 cards numbered 3, and 5
cards numbered 4.
7. 1. Construct a probability distribution for
drawing a card from a deck of 40cards consisting
of 10 cards numbered 1, 10 cards numbered 2,
15 cards numbered 3, and 5 cards numbered 4.
Cards 1 2 3 4
Number of Cards
Probability
8. 1. Construct a probability distribution for
drawing a card from a deck of 40cards consisting
of 10 cards numbered 1, 10 cards numbered 2,
15 cards numbered 3, and 5 cards numbered 4.
Cards 1 2 3 4
Number of Cards 10 10 15 5
Probability
9. 1. Construct a probability distribution for
drawing a card from a deck of 40cards consisting
of 10 cards numbered 1, 10 cards numbered 2,
15 cards numbered 3, and 5 cards numbered 4.
Cards 1 2 3 4
Number of Cards 10 10 15 5
Probability 0.25
10. 1. Construct a probability distribution for
drawing a card from a deck of 40cards consisting
of 10 cards numbered 1, 10 cards numbered 2,
15 cards numbered 3, and 5 cards numbered 4.
Cards 1 2 3 4
Number of Cards 10 10 15 5
Probability 0.25 0.25
11. 1. Construct a probability distribution for
drawing a card from a deck of 40cards consisting
of 10 cards numbered 1, 10 cards numbered 2,
15 cards numbered 3, and 5 cards numbered 4.
Cards 1 2 3 4
Number of Cards 10 10 15 5
Probability 0.25 0.25 0.375
12. 1. Construct a probability distribution for
drawing a card from a deck of 40cards consisting
of 10 cards numbered 1, 10 cards numbered 2,
15 cards numbered 3, and 5 cards numbered 4.
Cards 1 2 3 4
Number of Cards 10 10 15 5
Probability 0.25 0.25 0.375 0.125
13. Draw a probability histogram.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
P(1) P(2) P(3) P(4)
Series 1
Series 1
14. Example: Probability Distribution of
Random Variable
2. The following data represents the
enrollees of Ford Academy of the
Arts in grades 7 to 10 in the year
2019.
Grade Level 7 8 9 10
Enrollees 54 62 57 72
15. Example: Probability Distribution of
Random Variable
a) Construct a probability distribution
for a random variable.
b) Draw a probability histogram.
Grade Level 7 8 9 10
Enrollees 54 62 57 72
17. Definition
Mean (μ) – average value
- Expectation of random variable or
E(X)
E(X) or μ
Variance (σ2) – measures of spread
Standard Deviation (σ) – square root of the
variance
- measure of spread
20. Let the number of cards be x and probability of
the number of cards be p(x), then
Cards 1 2 3 4
Number of Cards (x) 10 10 15 5
Probability p(x) 0.25 0.25 0.375 0.125
21. Mean: μ = ∑ (x)[p(x)]
μ = ∑ (x)[p(x)]
Substitute the given.
μ = (10 x 0.25) + (10 x 0.25) + (15 x 0.375) + (5 x 0.125)
Multiply
μ = 2.5 + 2.5 + 5.625 + 0.625
Add
μ = 11.25
22. Using the frequency distribution table of
example 1, solve for the variance.