if 9 coins are tossed N (N a given number), construct the corresponding histogra
ID: 3135372 • Letter: I
Question
if 9 coins are tossed N (N a given number), construct the corresponding histogram for the theoretical frequency of 0,1,2,...,9 heads given below. in this case N=512. note that the fractions in the second columns are left unreduced on purpose.
x. f. expected(binomial)f
0. (1/512)N
1. (9/512)N
2. (36/512)N
3. (84/512)N
4. (126/512)N
5. (126/512)N
6. (84/512)N
7. (36/512)N
8. (9/512)N
9. (1/512)N
noting that the histogram is symmetric, calculate the mean and the standard deviation.
Explanation / Answer
If 9 coins are tossed N (N a given number), construct the corresponding histogram for the theoretical frequency of 0, 1, 2,..., 9 heads given below. In this case N=512. Note that the fractions in the second columns are left unreduced on purpose.
Noting that the histogram is symmetric, calculate the mean and the standard deviation.
Solution:
The table for the calculations purpose is given as below:
x
f
p
XP(x)
x - mean
(x - mean)^2
(x - mean)^2 * P(x)
0
1
0.001953125
0
-4.5
20.25
0.039550781
1
9
0.017578125
0.017578125
-3.5
12.25
0.215332031
2
36
0.0703125
0.140625
-2.5
6.25
0.439453125
3
84
0.1640625
0.4921875
-1.5
2.25
0.369140625
4
126
0.24609375
0.984375
-0.5
0.25
0.061523438
5
126
0.24609375
1.23046875
0.5
0.25
0.061523438
6
84
0.1640625
0.984375
1.5
2.25
0.369140625
7
36
0.0703125
0.4921875
2.5
6.25
0.439453125
8
9
0.017578125
0.140625
3.5
12.25
0.215332031
9
1
0.001953125
0.017578125
4.5
20.25
0.039550781
512
1
4.5
0
82.5
2.25
Mean = XP(X) = 4.5
Variance = (x - mean)^2 * P(x) = 2.25
Standard deviation = sqrt (2.25) = 1.5
x
f
p
XP(x)
x - mean
(x - mean)^2
(x - mean)^2 * P(x)
0
1
0.001953125
0
-4.5
20.25
0.039550781
1
9
0.017578125
0.017578125
-3.5
12.25
0.215332031
2
36
0.0703125
0.140625
-2.5
6.25
0.439453125
3
84
0.1640625
0.4921875
-1.5
2.25
0.369140625
4
126
0.24609375
0.984375
-0.5
0.25
0.061523438
5
126
0.24609375
1.23046875
0.5
0.25
0.061523438
6
84
0.1640625
0.984375
1.5
2.25
0.369140625
7
36
0.0703125
0.4921875
2.5
6.25
0.439453125
8
9
0.017578125
0.140625
3.5
12.25
0.215332031
9
1
0.001953125
0.017578125
4.5
20.25
0.039550781
512
1
4.5
0
82.5
2.25
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