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Question
Two fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X. Also find E(X).
Solution
Sample space S = {HH, HT, TH, TT}
n(S) = 4
Let x be the Random variable that "number of Heads".
The probability distribution is
| X = x | 0 | 1 | 2 |
| P( X = x ) | `1/4` | `2/4` | `1/4` |
∑ p(x) = `1/4 + 2/4 + 1/4 = 1`
∑ (x) = ∑ x. P (x)
= `x_1 p( x_1 ) + x_2 p( x_2 ) + x_3 p( x_3 )`
= `0 xx 1/4 + 1 xx 2/4 + 2 xx 1/4 `
= `1/4 [ 0 + 2 + 2 ] = 4/4 = 1`
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