grade 11 statistics and probability

1. Properties of Discrete
Probability Distribution

2. Review
Probability Distribution of a Discrete Random Variable
 It is a correspondence that assigns probabilities to the values of a random variable
 It is also called probability mass function
 It is a listing of the possible values and the corresponding probabilities of a
discrete random variable or a formula for the probabilities.

3.  In our examples, examine the probability distribution that we have obtained.
 What do you notice about the probability values of the random variable in each
probability distribution?
 What is the sum of the probabilities of a random variable?

4. Discuss the…
Properties of a discrete probability distribution
Example
Consider the probability distribution of the number of bananas given below.
Find the following.
1. P(R=3) 2. P(R=1) 3. P(R>1) 4. P(R<2) 5. 𝑃(𝑅)
R 3 2 1 0
P(R) 1
8
3
8
3
8
1
8

5. Observe from our examples that each probability value is less than or equal to one,
but greater than or equal to zero. Notice also that the sum of all probabilities is equal
to one.

6. Finding the Discrete Probability
Distribution Described by a Formula
Sometimes, discrete probability distributions are described by a formula. To ascertain
that a formula describes a probability distribution, we need to substitute the values of
the random variable in the formula, and the obtained values should satisfy the
properties of a probability distribution.

7. Example
 Determine whether or not the formula below describes a probability distribution.
P(X)=
𝑥+1
7
where X= 0,1,3. If it is, find the following:
1. P(X = 3)
2. P(X ≥ 1)
3. P(X ≤ 1)

8. Graphical Presentation of a Discrete
Probability Distribution
 The probability distribution of a discrete random variable can be shown graphically
by constructing a histogram. The graph is called a probability histogram.
 The probability histogram displays the possible values of a discrete random
variable on the horizontal axis and the probabilities of those values on the vertical
axis.

9. Example
 Construct the probability histogram of the probability distribution of the number of ripe bananas.
Probability Distribution of the Number of Ripe Bananas
R 3 2 1 0
P(R) 1
8
3
8
3
8
1
8

10. Next, this time, do this on your own. Draw
the bar graph for the given data.
Construct the probability histogram of the probability distribution of the number of heads.
Probability Distribution of the Number of Heads
H 2 1 0
P(H) 1
4
1
2
1
4

11. Summary of Key Ideas
 A probability distribution of discrete random variable is a correspondence that
assigns probabilities to the values of a random variable. The probability distribution
of a discrete random variable is also called the probability mass function.
 Probability distribution is a listing of the possible values and the corresponding
probabilities of a discrete random variable or a formula for the probabilities.
For any discrete random variable X, the following are true.
* 0 ≤ P(X) ≤ 1, for each value of X
* 𝑷(𝑿) =1

12.  A probability distribution can be described by a formula.
 The probability histogram is a bar graph that displays the possible values pf a
discrete random variable on the horizontal axis and the probabilities of those
values on the vertical axis.