Question

Two fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X. Also find E(X).

Answer 1

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`