2. โฆObjectives:
At the end of the lesson, the students will be able to:
โฆ define the probability distribution of discrete random variable;
โฆ familiarize themselves with the steps of constructing probability
distribution of discrete random variable;
โฆ construct probability distribution of discrete random variable.
6. ๐ฟ๐๐ก, ๐ = ๐๐ข๐๐๐๐ ๐๐ โ๐๐๐๐
๐ฅ = 0,1,2
Consider tossing two fair coins, and you record the number
of heads obtained.
x
Probability P(X=x)
๐ท๐๐๐ค ๐ข๐ ๐กโ๐ ๐๐๐๐๐๐๐๐๐๐ก๐ฆ ๐๐๐ ๐ก๐๐๐๐ข๐ก๐๐๐
0 1 2
1
4
2
4
1
4
๐๐๐ก๐๐
1
8. x 0 1 2 3 4 5
P(X=x)
๐
๐๐
๐๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
Two ordinary fair dice are thrown.
The resulting score is found as follows.
โข If the two dice show different numbers, the score is the smaller of the
two numbers.
โข If the two dice show equal numbers, the score is 0 .
Draw up the probability distribution for the score.
Example 1
x 1 2 3 4 5 6
1
2
3
4
5
6
9. At a garden centre, there is a display of roses:
25 are red
20 are white
15 are pink
5 are orange
Three roses are chosen at random.
๐. ๐ท๐๐๐ค ๐ข๐ ๐กโ๐ ๐๐๐๐๐๐๐๐๐๐ก๐ฆ ๐๐๐ ๐ก๐๐๐๐ข๐ก๐๐๐ ๐ก๐๐๐๐ ๐๐๐ ๐กโ๐ ๐๐ข๐๐๐๐ ๐๐
๐๐๐ ๐๐๐ ๐๐ ๐ ๐๐๐๐๐ก๐๐.
๐. ๐น๐๐๐ ๐กโ๐ ๐๐๐๐๐๐๐๐๐๐ก๐ฆ ๐กโ๐๐ก ๐๐ก ๐๐๐๐ ๐ก ๐๐๐ ๐๐๐ ๐๐๐ ๐ ๐๐ ๐ ๐๐๐๐๐ก๐๐.
๐ ๐ โฅ 1 = 0.446 + 0.275 + 0.0527 = 0.774
Example 2
10. 1 1 1 2 3
1
2
3
X
1 1 1 2 3
2 2 2 4 6
3 3 3 6 9
A fair 5 โ sided spinner has sides numbered 1,1,1,2,3. A fair three-sided has
sides numbered 1,2,3. Both spinners are spun once and the score is the
product of the numbers on the sides the spinners land on.
Draw up the probability distribution table for the score.
Example 3
11. A fair 4 โ sided die, numbered 1,2,3 and 5 is rolled twice.
The random variable X is the sum of the two numbers on which the
die comes to rest.
Draw up the probability distribution table for X and find P(X>6).
x
P(X=x)
+ 1 2 3 5
1
2
3
5
2 3 4 6
3 4 5 7
4 5 6 8
6 7 8 10
๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐
๐๐
๐. ๐ท ๐ฟ > ๐ = ๐ท ๐ฟ = ๐, ๐, ๐๐
=
๐
๐๐
Activity
12. Set A consists of ten digits 0,0,0,0,0,0,2,2,2,4
Set B consists of the seven digits 0,0,0,0,2,2,2
One digit is chosen at random from each set.
The random variable X is defined
as the sum of these two digits.
Draw up the probability distribution for the score.
Homework