1. 6.2/6.3 Probability Distributions and Distribution Mean
Advanced Math Topics
6.2/6.3 Probability Distributions and Distribution Mean

2. A discrete random variable.
# of Assignments
Turned in (x)
A continuous random variable would
have decimal values.
Probability
1/19 1
2/19 2
4/19 3
5/19 4
7/19
19/19 = 1
The probability total will always be 1.
This is an example of a probability distribution.

3. Create a probability distribution for the random
variable of x, the number of heads on three
coin flips.
# of Heads (x)
Probability
1/8 1
3/8
H H H
H H T
H T H 2
3/8
H T T
T T T 3
1/8
T T H
T H T
8/8 = 1
T H H

4. μ = Σ x • p(x) To find the mean of the probability distribution:
Find the mean of the probability distribution from the last slide.
# of Heads (x)
Probability
x • p(x)
1/8 1
3/8
3/8 2
3/8
6/8 3
1/8
3/8
μ = 12/8 = 1.5

5. From the HW P. 294
10) A farmer plants four seedlings. Let x be the number of seedlings that sprout.
Find the probability distribution of x. Assume that a seedling dying or sprouting
has equal probability.
# of Heads (x)
Probability
1/16 1
4/16 2
6/16 3
4/16 4
1/16
16/16 = 1

6. From the HW P. 306
1) Find the mean of the distribution.
# of Mail Pieces (x)
Probability
x • p(x)
0.02 1
0.03
0.03 2
0.25
0.5 3
0.19
0.57 4
0.16
0.64 5
0.14
0.70 6
0.12
0.72 7
0.08
0.56 8
0.01
0.08
μ = 3.8

7. HW
P. 295 #1-7, 10 , 11, P. 306 Compute the mean only for #1-4