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Question
Find the probability distribution of number of number of tails in three tosses of a coin
Solution
Let X denote the number of tails.
Sample space of the experiment is
S = {HHH, HHT, HTH, THH, TTT, TTH, THT, HTT}
The values of X corresponding to these outcomes are as follows.
X(HHH) = 0
X(HHT) = X(HTH) = X(THH) = 1
X(TTH) = X(THT) = X(HTT) = 2
X(TTT) = 3
∴ X is a discrete random variable that can take values 0, 1, 2, 3.
The probability distribution of X is then obtained as follows:
| X | 0 | 1 | 2 | 3 |
| P(X = x) | `(1)/(8)` | `(3)/(8)` | `(3)/(8)` | `(1)/(8)` |
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