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Toss 5 coins 25 times and note on each throw the number of heads. Make a...

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Statistics

Toss 5 coins 25 times and note on each throw the number ofheads. Make a probability distribution of the number of heads. Findmean and variance of that distribution and compare it with the meanand variance of theoretical probability distribution using binomialprobability distribution.

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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
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