Four coins were tossed and number of heads noted. The experiment is repeated 200 times. The number of tosses showing 0, 1, 2, 3 and 4 heads were found distributed as under. Fit a binomial distribution to these observed results assuming that the nature of the coins is not known.
| Number of Heads | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Number of Tosses | 15 | 35 | 90 | 40 | 20 |
We are asked to fit a binomial distribution for four coins tossed 200 times with observed frequencies of heads. Let the probability of getting a head on a single coin be (p). For (n = 4) coins, the binomial probability is [ P(X = k) = \binom{4}{k} p^k (1-p)^{4-k}, \quad k = 0,1,2,3,4. ] The observed frequencies are: 0 → 15, 1 → 35, 2 → 90, 3 → 40, 4 → ________ _____ _______ __________ _________ ___ __________ ________.
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.
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Four coins were tossed and number of heads noted. The experiment is repeated 200 times. The number of tosses showing 0, 1, 2, 3 and 4 heads were found distributed as under. Fit a binomial distribution to these observed results assuming that the nature of the coins is not known.
| Number of Heads | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Number of Tosses | 15 | 35 | 90 | 40 | 20 |
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