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Using Example 4 in the previous page,
Steps Solution
1. List the sample space S = { HHHH, HHHT, HHTH, HHTT,
HTHH, HTHT, HTTH, HTTT, THHH,
THHT, THTH, THTT, TTHH, TTHT,
TTTH, TTTT }
2. Count the
number of tails in
each outcome and
assign this number
to this outcome.
HHHH 0
HHHT 1
HHTH 1
HHTT 2
HTHH 1
HTHT 2
Outcome
Number of tails
(Value of T)
HTTH 2
HTTT 3
THHH 1
THHT 2
THTH 2
THTT 3
TTHH 2
TTHT 3
TTTH 3
TTTT 4
The value of the random variable T
(number of tails) in this experiment
are 0, 1, 2, 3 and 4.
3. Construct the
frequency distribution
of the values of the
random variable T.
0 1
1 4
2 6
3 4
4 1
Total 16
Number of Tails
(Value of T)
Number of Occurrence
(Frequency)
4. Construct the
probability distribution of
the random variable T by
getting the probability of
occurrence of each value
of the random variable
0 1 1/16
1 4 4/16 or 1/4
2 6 6/16 or 3/8
3 4 4/16 or 1/4
4 1 1/16
Total 16 1
(Value of T) (Frequency)
Probability
P(T)
The probability distribution of the random variable
T can be written as follows:
T 0 1 2 3 4
P(T) 1/16 1/4 3/8 1/4 1/16
5. Construct the probability
histogram
P(T)
0 1 2 3 4
0
2
4
6
8
10
12
14
16
T
Using Example 5 in the previous page,
Steps Solution
1. List the sample space S=
{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4,), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
2. Count the sum of the
number of dots in each
outcome and assign this
number to this outcome.
Sum of the numbe
of dots (Value of X
Outcome
(1,6),(6,1),(2,5),(5,2),(4,3),(3,
4)
(1,5),(5,1),(2,4),(4,2),(3,3)
(1,4), (4,1), (2,3), (3,2)
(1,3), (3,1), (2,2)
(1,2), (2,1)
(1,1) 2
3
4
5
6
7
(3,5), (5,3), (2,6), (6,2), (4,4)
(5,4), (4,5), (6,3), (3,6)
(6,4), (4,6), (5,5)
(5,6), (6,5)
(6,6) 12
11
10
9
8
The value of the random variable X (sum of the number of dots) in
this experiment are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
3. Construct the
frequency distribution of
the values of the random
variable X.
(Value of X) (Frequency)
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
5
4
3
2
1
Total 36
4. Construct the
probability distribution
of the random variable
X by getting the
probability of
occurrence of each
value of the random
variable.
3
Some of the number
of dots (Value of X)
2
Number of Occurrence
(Frequency) Probability P(X)
4
5
6
7
1
2
3
4
5
6
1/36
2/36 or 1/18
3/36 or 1/12
4/36 or 1/9
5/36
6/36 or 1/6
8
9
10
11
12
Total
5
4
3
2
1
36
5/36
4/36 or 1/9
3/36 or 1/12
2/36 or 1/18
1/36
1
The probability distribution of the random variable X
can be written as follows:
X
P(X)
2
1/36
3 4 5 6 7 8 9 10 11 12
1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36
5. Construct the probability
histogram.
2 3 4 5 6 7 8 9 10 11 12
0
9
18
27
36
X
P(X)
Thank You!

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Report.pptx

  • 1. Using Example 4 in the previous page, Steps Solution 1. List the sample space S = { HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT }
  • 2. 2. Count the number of tails in each outcome and assign this number to this outcome. HHHH 0 HHHT 1 HHTH 1 HHTT 2 HTHH 1 HTHT 2 Outcome Number of tails (Value of T)
  • 3. HTTH 2 HTTT 3 THHH 1 THHT 2 THTH 2 THTT 3 TTHH 2 TTHT 3 TTTH 3 TTTT 4 The value of the random variable T (number of tails) in this experiment are 0, 1, 2, 3 and 4.
  • 4. 3. Construct the frequency distribution of the values of the random variable T. 0 1 1 4 2 6 3 4 4 1 Total 16 Number of Tails (Value of T) Number of Occurrence (Frequency)
  • 5. 4. Construct the probability distribution of the random variable T by getting the probability of occurrence of each value of the random variable 0 1 1/16 1 4 4/16 or 1/4 2 6 6/16 or 3/8 3 4 4/16 or 1/4 4 1 1/16 Total 16 1 (Value of T) (Frequency) Probability P(T) The probability distribution of the random variable T can be written as follows: T 0 1 2 3 4 P(T) 1/16 1/4 3/8 1/4 1/16
  • 6. 5. Construct the probability histogram P(T) 0 1 2 3 4 0 2 4 6 8 10 12 14 16 T
  • 7. Using Example 5 in the previous page, Steps Solution 1. List the sample space S= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4,), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
  • 8. 2. Count the sum of the number of dots in each outcome and assign this number to this outcome. Sum of the numbe of dots (Value of X Outcome (1,6),(6,1),(2,5),(5,2),(4,3),(3, 4) (1,5),(5,1),(2,4),(4,2),(3,3) (1,4), (4,1), (2,3), (3,2) (1,3), (3,1), (2,2) (1,2), (2,1) (1,1) 2 3 4 5 6 7
  • 9. (3,5), (5,3), (2,6), (6,2), (4,4) (5,4), (4,5), (6,3), (3,6) (6,4), (4,6), (5,5) (5,6), (6,5) (6,6) 12 11 10 9 8 The value of the random variable X (sum of the number of dots) in this experiment are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
  • 10. 3. Construct the frequency distribution of the values of the random variable X. (Value of X) (Frequency) 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 5 4 3 2 1 Total 36
  • 11. 4. Construct the probability distribution of the random variable X by getting the probability of occurrence of each value of the random variable. 3 Some of the number of dots (Value of X) 2 Number of Occurrence (Frequency) Probability P(X) 4 5 6 7 1 2 3 4 5 6 1/36 2/36 or 1/18 3/36 or 1/12 4/36 or 1/9 5/36 6/36 or 1/6
  • 12. 8 9 10 11 12 Total 5 4 3 2 1 36 5/36 4/36 or 1/9 3/36 or 1/12 2/36 or 1/18 1/36 1 The probability distribution of the random variable X can be written as follows: X P(X) 2 1/36 3 4 5 6 7 8 9 10 11 12 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36
  • 13. 5. Construct the probability histogram. 2 3 4 5 6 7 8 9 10 11 12 0 9 18 27 36 X P(X)