|
Toss |
Coin 1 |
Coin 2 |
Coin 3 |
Coin 4 |
Coin 5 |
# of Heads |
|
1 |
1 |
1 |
0 |
0 |
0 |
3 |
|
2 |
1 |
0 |
0 |
1 |
1 |
2 |
|
3 |
1 |
0 |
1 |
0 |
0 |
3 |
|
4 |
1 |
0 |
1 |
1 |
1 |
1 |
|
5 |
1 |
0 |
0 |
1 |
0 |
3 |
|
6 |
1 |
1 |
0 |
1 |
0 |
2 |
|
7 |
1 |
0 |
1 |
1 |
0 |
2 |
|
8 |
1 |
0 |
0 |
1 |
1 |
2 |
|
9 |
0 |
0 |
0 |
1 |
0 |
4 |
|
10 |
1 |
1 |
1 |
0 |
0 |
2 |
|
11 |
1 |
1 |
0 |
1 |
0 |
2 |
|
12 |
0 |
1 |
0 |
0 |
0 |
4 |
|
13 |
1 |
0 |
1 |
1 |
0 |
2 |
|
14 |
1 |
0 |
0 |
0 |
0 |
4 |
|
15 |
1 |
0 |
0 |
0 |
0 |
4 |
|
16 |
0 |
0 |
1 |
1 |
1 |
2 |
|
17 |
0 |
1 |
0 |
0 |
0 |
4 |
|
18 |
0 |
1 |
1 |
0 |
0 |
3 |
|
19 |
1 |
1 |
1 |
0 |
1 |
1 |
|
20 |
1 |
0 |
0 |
1 |
1 |
2 |
|
21 |
0 |
1 |
0 |
0 |
1 |
3 |
|
22 |
0 |
0 |
0 |
0 |
0 |
5 |
|
23 |
0 |
0 |
0 |
1 |
0 |
4 |
|
24 |
0 |
1 |
0 |
1 |
1 |
2 |
|
25 |
0 |
0 |
0 |
1 |
0 |
4 |
|
# of Heads (x) |
Frequency |
Probability P(x) |
|
0 |
0 |
0 |
|
1 |
2 |
0.08 |
|
2 |
10 |
0.4 |
|
3 |
5 |
0.2 |
|
4 |
7 |
0.28 |
|
5 |
1 |
0.04 |
Mean = ∑x * P(x) = 2.8
Variance = ∑(x^2) P(x) - Mean^2 = 1.12
For the theoretical binomial distribution, mean = np = 5 * (1/2)
= 2.5 and variance = np(1 - p) = 5 * (1/2) * (1/2) = 1.25
