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Question
Find the probability distribution of number of heads in four tosses of a coin
Solution
Let X denote the number of heads.
Sample space of the experiment is
S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, TTHH, THTH, HTHT, THHT, HTTT, THTT, TTHT, TTTH, TTTT}
The values of X corresponding to these outcomes are as follows.
X(TTTT) = 0
X(HTTT) = X(THTT) = X(TTHT) = X(TTTH) = 1
X(HHTT) = X(HTTH) = X(TTHH) = X(THTH) = X(HTHT) = X(THHT) = 2
X(HHHT) = X(HHTH) = X(HTHH) = X(THHH) = 3
X(HHHH) = 4
∴ X is a discrete random variable that can take values 0, 1, 2, 3, 4.
The probability distribution of X is then obtained as follows:
| X | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | `(1)/(16)` | `(4)/(16)` | `(6)/(16)` | `(4)/(16)` | `(1)/(16)` |
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